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User:Jon Awbrey/SEQUENCES (view source)
Revision as of 08:33, 11 January 2010
, 08:33, 11 January 2010→A106177
<p><math>a(6) ~=~ 30</math></p>
<p><math>a(6) ~=~ 30</math></p>
|}
|}
==A106177==
* [http://oeis.org/wiki/A106177 A106177]
===Primal Codes of Finite Partial Functions on Positive Integers===
{| align="center"
|
<math>\begin{array}{rcl}
1 & = & \varnothing \\
2 & = & 1\!:\!1 \\
3 & = & 2\!:\!1 \\
4 & = & 1\!:\!2 \\
5 & = & 3\!:\!1 \\
6 & = & 1\!:\!1 ~~ 2\!:\!1 \\
7 & = & 4\!:\!1 \\
8 & = & 1\!:\!3 \\
9 & = & 2\!:\!2 \\
10 & = & 1\!:\!1 ~~ 3\!:\!1 \\
11 & = & 5\!:\!1 \\
12 & = & 1\!:\!2 ~~ 2\!:\!1 \\
13 & = & 6\!:\!1 \\
14 & = & 1\!:\!1 ~~ 4\!:\!1 \\
15 & = & 2\!:\!1 ~~ 3\!:\!1 \\
16 & = & 1\!:\!4 \\
17 & = & 7\!:\!1 \\
18 & = & 1\!:\!1 ~~ 2\!:\!2 \\
19 & = & 8\!:\!1 \\
20 & = & 1\!:\!2 ~~ 3\!:\!1
\end{array}</math>
|}
===Wiki Table===
{| align="center" style="font-weight:bold; text-align:center"
| || || || || || || || ||
| <font color="red">1</font>
|
| <font color="red">1</font>
|-
| || || || || || || ||
| <font color="red">2</font>
| || 1 ||
| <font color="red">2</font>
|-
| || || || || || ||
| <font color="red">3</font>
| || 1 || || 1 ||
| <font color="red">3</font>
|-
| || || || || ||
| <font color="red">4</font>
| || 1 || || 2 || || 1 ||
| <font color="red">4</font>
|-
| || || || ||
| <font color="red">5</font>
| || 1 || || 3 || || 1 || || 1 ||
| <font color="red">5</font>
|-
| || || ||
| <font color="red">6</font>
| || 1 || || 1 || || 1 || || 4 || || 1 ||
| <font color="red">6</font>
|-
| || ||
| <font color="red">7</font>
| || 1 || || 5 || || 2 || || 9 || || 1 || || 1 ||
| <font color="red">7</font>
|-
| ||
| <font color="red">8</font>
| || 1 || || 6 || || 1 || || 1 || || 1 || || 2 || || 1 ||
| <font color="red">8</font>
|-
|
| <font color="red">9</font>
| || 1 || || 7 || || 1 || || 25|| || 1 || || 3 || || 1 || || 1 ||
| <font color="red">9</font>
|-
| width="12pt" | <font color="red">10</font>
| width="12pt" |
| width="12pt" | 1
| width="12pt" |
| width="12pt" | 1
| width="12pt" |
| width="12pt" | 1
| width="12pt" |
| width="12pt" | 36
| width="12pt" |
| width="12pt" | 1
| width="12pt" |
| width="12pt" | 2
| width="12pt" |
| width="12pt" | 1
| width="12pt" |
| width="12pt" | 8
| width="12pt" |
| width="12pt" | 1
| width="12pt" |
| width="12pt" | <font color="red">10</font>
|}
===Wiki + TeX===
====Smallmatrix====
{| align="center"
|
<math>\begin{smallmatrix}
& & & & & & & & & {\color{red}1} & & {\color{red}1}
\\
& & & & & & & & {\color{red}2} & & 1 & & {\color{red}2}
\\
& & & & & & & {\color{red}3} & & 1 & & 1 & & {\color{red}3}
\\
& & & & & & {\color{red}4} & & 1 & & 2 & & 1 & & {\color{red}4}
\\
& & & & & {\color{red}5} & & 1 & & 3 & & 1 & & 1 & & {\color{red}5}
\\
& & & & {\color{red}6} & & 1 & & 1 & & 1 & & 4 & & 1 & & {\color{red}6}
\\
& & & {\color{red}7} & & 1 & & 5 & & 2 & & 9 & & 1 & & 1 & & {\color{red}7}
\\
& & {\color{red}8} & & 1 & & 6 & & 1 & & 1 & & 1 & & 2 & & 1 & & {\color{red}8}
\\
& {\color{red}9} & & 1 & & 7 & & 1 & & 25 & & 1 & & 3 & & 1 & & 1 & & {\color{red}9}
\\
{\color{red}10} & & 1 & & 1 & & 1 & & 36 & & 1 & & 2 & & 1 & & 8 & & 1 & & {\color{red}10}
\end{smallmatrix}</math>
|}
====Array====
{| align="center"
|
<math>\begin{array}{*{21}{c}}
& & & & & & & & & {\color{red}1} & & {\color{red}1}
\\
& & & & & & & & {\color{red}2} & & 1 & & {\color{red}2}
\\
& & & & & & & {\color{red}3} & & 1 & & 1 & & {\color{red}3}
\\
& & & & & & {\color{red}4} & & 1 & & 2 & & 1 & & {\color{red}4}
\\
& & & & & {\color{red}5} & & 1 & & 3 & & 1 & & 1 & & {\color{red}5}
\\
& & & & {\color{red}6} & & 1 & & 1 & & 1 & & 4 & & 1 & & {\color{red}6}
\\
& & & {\color{red}7} & & 1 & & 5 & & 2 & & 9 & & 1 & & 1 & & {\color{red}7}
\\
& & {\color{red}8} & & 1 & & 6 & & 1 & & 1 & & 1 & & 2 & & 1 & & {\color{red}8}
\\
& {\color{red}9} & & 1 & & 7 & & 1 & & 25 & & 1 & & 3 & & 1 & & 1 & & {\color{red}9}
\\
{\color{red}10} & & 1 & & 1 & & 1 & & 36 & & 1 & & 2 & & 1 & & 8 & & 1 & & {\color{red}10}
\end{array}</math>
|}
====Matrix====
{| align="center"
|
<math>\begin{matrix}
n \circ m
\\
1 ~/~\backslash~ 1
\\
2 ~/~ 1 ~\backslash~ 2
\\
3 ~/~ 1 \cdot 1 ~\backslash~ 3
\\
4 ~/~ 1 \cdot 2 \cdot 1 ~\backslash~ 4
\\
5 ~/~ 1 \cdot 3 \cdot 1 \cdot 1 ~\backslash~ 5
\\
6 ~/~ 1 \cdot 1 \cdot 1 \cdot 4 \cdot 1 ~\backslash~ 6
\\
7 ~/~ 1 \cdot 5 \cdot 2 \cdot 9 \cdot 1 \cdot 1 ~\backslash~ 7
\\
8 ~/~ 1 \cdot 6 \cdot 1 \cdot 1 \cdot 1 \cdot 2 \cdot 1 ~\backslash~ 8
\\
9 ~/~ 1 \cdot 7 \cdot 1 \cdot 25\cdot 1 \cdot 3 \cdot 1 \cdot 1 ~\backslash~ 9
\\
10 ~/~ 1 \cdot 1 \cdot 1 \cdot 36\cdot 1 \cdot 2 \cdot 1 \cdot 8 \cdot 1 ~\backslash~ 10
\end{matrix}</math>
|}
===ASCII===
<pre>
Example
* n o m
* \ /
* 1 . 1
* \ / \ /
* 2 . 1 . 2
* \ / \ / \ /
* 3 . 1 . 1 . 3
* \ / \ / \ / \ /
* 4 . 1 . 2 . 1 . 4
* \ / \ / \ / \ / \ /
* 5 . 1 . 3 . 1 . 1 . 5
* \ / \ / \ / \ / \ / \ /
* 6 . 1 . 1 . 1 . 4 . 1 . 6
* \ / \ / \ / \ / \ / \ / \ /
* 7 . 1 . 5 . 2 . 9 . 1 . 1 . 7
* \ / \ / \ / \ / \ / \ / \ / \ /
* 8 . 1 . 6 . 1 . 1 . 1 . 2 . 1 . 8
* \ / \ / \ / \ / \ / \ / \ / \ / \ /
* 9 . 1 . 7 . 1 . 25. 1 . 3 . 1 . 1 . 9
* \ / \ / \ / \ / \ / \ / \ / \ / \ / \ /
* 10 . 1 . 1 . 1 . 36. 1 . 2 . 1 . 8 . 1 . 10
*
* Primal codes of finite partial functions on positive integers:
* 1 = { }
* 2 = 1:1
* 3 = 2:1
* 4 = 1:2
* 5 = 3:1
* 6 = 1:1 2:1
* 7 = 4:1
* 8 = 1:3
* 9 = 2:2
* 10 = 1:1 3:1
* 11 = 5:1
* 12 = 1:2 2:1
* 13 = 6:1
* 14 = 1:1 4:1
* 15 = 2:1 3:1
* 16 = 1:4
* 17 = 7:1
* 18 = 1:1 2:2
* 19 = 8:1
* 20 = 1:2 3:1
</pre>
==A109300==
==A109300==