cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A112846 Number of riffs on n or fewer nodes. Number of rotes on 2n+1 or fewer nodes.

Original entry on oeis.org

1, 2, 4, 10, 30, 103, 384, 1508, 6126, 25513, 108278, 466523, 2034981, 8968746, 39875940, 138760603, 178636543, 3026583484, 16028356176, 75647274620, 350111055991, 1618175863400, 7495933933620, 34821723061950
Offset: 0

Views

Author

Jon Awbrey, Oct 04 2005, based on calculations by Vladeta Jovovic and David W. Wilson

Keywords

Comments

Partial sums of A061396.

Links

Crossrefs

Cf. A000079, A001221, A007097, A014221, A050924.
Cf. A061396, A062504, A062537, A062860, A106177.
Cf. A109300, A109301, A111791 to A111800.
Cf. A112095, A112096, A112480, A112481.

A112096 Tetrahedron T(g, h, w) = number of rotes of weight g, height h, wayage w.

Original entry on oeis.org

1, 1, 2, 1, 1, 4, 2, 8, 2, 8, 1, 12, 12, 28, 4, 16
Offset: 1

Views

Author

Jon Awbrey, Sep 08 2005, revised Sep 27 2005

Keywords

Comments

T(g, h, w) = |{m : A062537(m) = g, A109301(m) = h, A001221(m) = w}|.
This is the column that is labeled "r" in the tabulation of A112095.
g = h > 0 implies w = 1 and T(j, j, 1) = 2^(j-1) = A000079(j-1).

Examples

			Table T(g, h, w), omitting empty cells, starts out as follows:
g\(h,w) | (0,0) (1,1) (2,1) (2,2) (3,1) (3,2) (4,1) (4,2) (5,1)
--------+-------------------------------------------------------
0 ` ` ` | ` 1
1 ` ` ` | ` ` ` ` 1
2 ` ` ` | ` ` ` ` ` ` ` 2
3 ` ` ` | ` ` ` ` ` ` ` 1 ` ` 1 ` ` 4
4 ` ` ` | ` ` ` ` ` ` ` ` ` ` 2 ` ` 8 ` ` 2 ` ` 8
5 ` ` ` | ` ` ` ` ` ` ` ` ` ` 1 ` `12 ` `12 ` `28 ` ` 4 ` `16

Links

Crossrefs

Cf. A000079, A001221, A007097, A014221, A050924.
Cf. A061396, A062504, A062537, A062860, A106177.
Cf. A109300, A109301, A111791 to A111800, A112095.

A111798 Positive integers sorted by rote height (A109301) and omega (A001221).

Original entry on oeis.org

1, 2, 3, 4, 9, 6, 12, 18, 36, 5, 7, 8, 13, 16, 23, 25, 27, 37, 49, 61, 64, 81, 125, 151, 169, 343, 512, 529, 625, 729, 1369, 2197, 2401, 3721, 4096, 12167, 15625, 19683, 22801, 28561, 50653, 117649, 226981, 262144, 279841, 531441, 1874161, 1953125, 3442951
Offset: 1

Views

Author

Jon Awbrey, Sep 01 2005 - Sep 10 2005

Keywords

Comments

Positive integers m sorted by h(m) = A109301(m) and w(m) = A001221(m).
Defining the "wayage" of a rooted tree to be its root degree, the rote corresponding to the positive integer m has a wayage of w(m) = omega(m) = A001221(m).

Examples

			Table of Primal Functions, Codes, Sort Parameters and Subtotals
Primal Function | ` ` ` ` ` Primal Code ` ` = ` ` a | h w | s | t
----------------+-----------------------------------+-----+---+---
{ } ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 1 | 0 0 | 1 | 1
----------------+-----------------------------------+-----+---+---
1:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 2 | 1 1 | 1 | 1
----------------+-----------------------------------+-----+---+---
2:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 3 | 2 1 | ` |
1:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 4 | 2 1 | ` |
2:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 9 | 2 1 | 3 |
----------------+-----------------------------------+-----+---+---
1:1 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 6 | 2 2 | ` |
1:2 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `12 | 2 2 | ` |
1:1 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `18 | 2 2 | ` |
1:2 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `36 | 2 2 | 4 | 7
----------------+-----------------------------------+-----+---+---
` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |
1:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 8 | 3 1 | ` |
1:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `16 | 3 1 | ` |
1:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `64 | 3 1 | ` |
1:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 512 | 3 1 | ` |
1:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` `4096 | 3 1 | ` |
1:18` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `262144 | 3 1 | ` |
1:36` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 68719476736 | 3 1 | ` |
` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |
2:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `27 | 3 1 | ` |
2:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `81 | 3 1 | ` |
2:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 729 | 3 1 | ` |
2:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 19683 | 3 1 | ` |
2:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `531441 | 3 1 | ` |
2:18` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 387420489 | 3 1 | ` |
2:36` ` ` ` ` ` | ` ` ` ` ` ` ` `150094635296999121 | 3 1 | ` |
` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |
3:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 5 | 3 1 | ` |
4:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 7 | 3 1 | ` |
6:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `13 | 3 1 | ` |
9:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `23 | 3 1 | ` |
12:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `37 | 3 1 | ` |
18:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `61 | 3 1 | ` |
36:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 151 | 3 1 | ` |
` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |
3:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `25 | 3 1 | ` |
4:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `49 | 3 1 | ` |
6:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 169 | 3 1 | ` |
9:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 529 | 3 1 | ` |
12:2` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` `1369 | 3 1 | ` |
18:2` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` `3721 | 3 1 | ` |
36:2` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 22801 | 3 1 | ` |
` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |
3:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 125 | 3 1 | ` |
3:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 625 | 3 1 | ` |
3:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 15625 | 3 1 | ` |
3:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 1953125 | 3 1 | ` |
3:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 244140625 | 3 1 | ` |
3:18` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 3814697265625 | 3 1 | ` |
3:36` ` ` ` ` ` | ` ` ` `14551915228366851806640625 | 3 1 | ` |
` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |
4:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` 343 | 3 1 | ` |
4:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` `2401 | 3 1 | ` |
4:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `117649 | 3 1 | ` |
4:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` `40353607 | 3 1 | ` |
4:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 13841287201 | 3 1 | ` |
4:18` ` ` ` ` ` | ` ` ` ` ` ` ` ` `1628413597910449 | 3 1 | ` |
4:36` ` ` ` ` ` | ` 2651730845859653471779023381601 | 3 1 | ` |
` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |
6:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` `2197 | 3 1 | ` |
6:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 28561 | 3 1 | ` |
6:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 4826809 | 3 1 | ` |
6:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 10604499373 | 3 1 | ` |
6:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `23298085122481 | 3 1 | ` |
6:18` ` ` ` ` ` | ` ` ` ` ` ` 112455406951957393129 | 3 1 | ` |
6:36` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 13^36 | 3 1 | ` |
` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |
9:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 12167 | 3 1 | ` |
9:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `279841 | 3 1 | ` |
9:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 148035889 | 3 1 | ` |
9:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 1801152661463 | 3 1 | ` |
9:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` 21914624432020321 | 3 1 | ` |
9:18` ` ` ` ` ` | ` ` ` ` 3244150909895248285300369 | 3 1 | ` |
9:36` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 23^36 | 3 1 | ` |
` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |
12:3` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 50653 | 3 1 | ` |
12:4` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 1874161 | 3 1 | ` |
12:6` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `2565726409 | 3 1 | ` |
12:9` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` 129961739795077 | 3 1 | ` |
12:12 ` ` ` ` ` | ` ` ` ` ` ` ` 6582952005840035281 | 3 1 | ` |
12:18 ` ` ` ` ` | ` ` 16890053810563300749953435929 | 3 1 | ` |
12:36 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 37^36 | 3 1 | ` |
` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |
18:3` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `226981 | 3 1 | ` |
18:4` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` `13845841 | 3 1 | ` |
18:6` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 51520374361 | 3 1 | ` |
18:9` ` ` ` ` ` | ` ` ` ` ` ` ` ` 11694146092834141 | 3 1 | ` |
18:12 ` ` ` ` ` | ` ` ` ` ` `2654348974297586158321 | 3 1 | ` |
18:18 ` ` ` ` ` | 136753052840548005895349735207881 | 3 1 | ` |
18:36 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` 61^36 | 3 1 | ` |
` ` ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` | ` ` | ` |
36:3` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 3442951 | 3 1 | ` |
36:4` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 519885601 | 3 1 | ` |
36:6` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `11853911588401 | 3 1 | ` |
36:9` ` ` ` ` ` | ` ` ` ` ` ` `40812436757196811351 | 3 1 | ` |
36:12 ` ` ` ` ` | ` ` ` 140515219945627518837736801 | 3 1 | ` |
36:18 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `151^18 | 3 1 | ` |
36:36 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` `151^36 | 3 1 |77 |
----------------+-----------------------------------+-----+---+---
The last part is left unsorted to show the method of construction.
a (when sorted ) = this sequence
h = rote height in gammas = A109301
w = rote wayage in gammas = A001221
s = count in (h, w) class = A111799
t = count in height class = A109300

Links

Crossrefs

Cf. A000079, A001221, A007097, A014221, A050924.
Cf. A061396, A062504, A062537, A062860, A106177.
Cf. A109300, A109301, A111791 to A111800, A112095, A112096.

A112480 Positive integers sorted by rote weight, rote wagage and rote height.

Original entry on oeis.org

1, 2, 3, 4, 9, 5, 7, 8, 16, 6, 13, 23, 25, 27, 49, 64, 81, 512, 11, 17, 19, 32, 53, 128, 256, 65536, 12, 18, 10, 14, 37, 61, 125, 169, 343, 529, 625, 729, 2401, 4096, 19683, 262144, 29, 41, 43, 83, 97, 103, 121, 227, 243, 289, 311, 361, 419, 1024, 2187, 2809, 3671
Offset: 1

Views

Author

Jon Awbrey, Sep 27 2005

Keywords

Comments

For positive integer m, the rote weight in gammas is g(m) = A062537(m), the rote wayage or root degree is w(m) = omega(m) = A001221(m) and the rote height in gammas is h(m) = A109301(m).

Examples

			Table of Primal Functions, Codes, Sort Parameters and Subtotals
================================================================
Primal Function | ` ` ` Primal Code ` = ` a | g w h | r | s | t
================================================================
{ } ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 1 | 0 0 0 | 1 | 1 | 1
================================================================
1:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 2 | 1 1 1 | 1 | 1 | 1
================================================================
2:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 3 | 2 1 2 | ` | ` |
1:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 4 | 2 1 2 | 2 | 2 | 2
================================================================
2:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 9 | 3 1 2 | 1 | ` |
----------------+---------------------------+-------+---+---+---
3:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 5 | 3 1 3 | ` | ` |
4:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 7 | 3 1 3 | ` | ` |
1:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 8 | 3 1 3 | ` | ` |
1:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `16 | 3 1 3 | 4 | 5 |
----------------+---------------------------+-------+---+---+---
1:1 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` 6 | 3 2 2 | 1 | 1 | 6
================================================================
6:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `13 | 4 1 3 | ` | ` |
9:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `23 | 4 1 3 | ` | ` |
3:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `25 | 4 1 3 | ` | ` |
2:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `27 | 4 1 3 | ` | ` |
4:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `49 | 4 1 3 | ` | ` |
1:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `64 | 4 1 3 | ` | ` |
2:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `81 | 4 1 3 | ` | ` |
1:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 512 | 4 1 3 | 8 | ` |
----------------+---------------------------+-------+---+---+---
5:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `11 | 4 1 4 | ` | ` |
7:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `17 | 4 1 4 | ` | ` |
8:1 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `19 | 4 1 4 | ` | ` |
1:5 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `32 | 4 1 4 | ` | ` |
16:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `53 | 4 1 4 | ` | ` |
1:7 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 128 | 4 1 4 | ` | ` |
1:8 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 256 | 4 1 4 | ` | ` |
1:16` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 65536 | 4 1 4 | 8 |16 |
----------------+---------------------------+-------+---+---+---
1:2 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `12 | 4 2 2 | ` | ` |
1:1 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `18 | 4 2 2 | 2 | ` |
----------------+---------------------------+-------+---+---+---
1:1 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `10 | 4 2 3 | ` | ` |
1:1 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `14 | 4 2 3 | 2 | 4 |20
================================================================
12:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `37 | 5 1 3 | ` | ` |
18:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `61 | 5 1 3 | ` | ` |
3:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 125 | 5 1 3 | ` | ` |
6:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 169 | 5 1 3 | ` | ` |
4:3 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 343 | 5 1 3 | ` | ` |
9:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 529 | 5 1 3 | ` | ` |
3:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 625 | 5 1 3 | ` | ` |
2:6 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 729 | 5 1 3 | ` | ` |
4:4 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `2401 | 5 1 3 | ` | ` |
1:12` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `4096 | 5 1 3 | ` | ` |
2:9 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 19683 | 5 1 3 | ` | ` |
1:18` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `262144 | 5 1 3 |12 | ` |
----------------+---------------------------+-------+---+---+---
10:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `29 | 5 1 4 | ` | ` |
13:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `41 | 5 1 4 | ` | ` |
14:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `43 | 5 1 4 | ` | ` |
23:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `83 | 5 1 4 | ` | ` |
25:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `97 | 5 1 4 | ` | ` |
27:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 103 | 5 1 4 | ` | ` |
5:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 121 | 5 1 4 | ` | ` |
49:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 227 | 5 1 4 | ` | ` |
2:5 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 243 | 5 1 4 | ` | ` |
7:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 289 | 5 1 4 | ` | ` |
64:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 311 | 5 1 4 | ` | ` |
8:2 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 361 | 5 1 4 | ` | ` |
81:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 419 | 5 1 4 | ` | ` |
1:10` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `1024 | 5 1 4 | ` | ` |
2:7 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `2187 | 5 1 4 | ` | ` |
16:2` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `2809 | 5 1 4 | ` | ` |
512:1 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `3671 | 5 1 4 | ` | ` |
2:8 ` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `6561 | 5 1 4 | ` | ` |
1:13` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `8192 | 5 1 4 | ` | ` |
1:14` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 16384 | 5 1 4 | ` | ` |
1:23` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` 8388608 | 5 1 4 | ` | ` |
1:25` ` ` ` ` ` | ` ` ` ` ` ` ` ` `33554432 | 5 1 4 | ` | ` |
2:16` ` ` ` ` ` | ` ` ` ` ` ` ` ` `43046721 | 5 1 4 | ` | ` |
1:27` ` ` ` ` ` | ` ` ` ` ` ` ` ` 134217728 | 5 1 4 | ` | ` |
1:49` ` ` ` ` ` | ` ` ` ` ` 562949953421312 | 5 1 4 | ` | ` |
1:64` ` ` ` ` ` | ` ` `18446744073709551616 | 5 1 4 | ` | ` |
1:81` ` ` ` ` ` | 2417851639229258349412352 | 5 1 4 | ` | ` |
1:512 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 2^512 | 5 1 4 |28 | ` |
----------------+---------------------------+-------+---+---+---
11:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `31 | 5 1 5 | ` | ` |
17:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `59 | 5 1 5 | ` | ` |
19:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `67 | 5 1 5 | ` | ` |
32:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 131 | 5 1 5 | ` | ` |
53:1` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 241 | 5 1 5 | ` | ` |
128:1 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 719 | 5 1 5 | ` | ` |
256:1 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `1619 | 5 1 5 | ` | ` |
1:11` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` `2048 | 5 1 5 | ` | ` |
1:17` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `131072 | 5 1 5 | ` | ` |
1:19` ` ` ` ` ` | ` ` ` ` ` ` ` ` ` `524288 | 5 1 5 | ` | ` |
65536:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` `821641 | 5 1 5 | ` | ` |
1:32` ` ` ` ` ` | ` ` ` ` ` ` ` `4294967296 | 5 1 5 | ` | ` |
1:53` ` ` ` ` ` | ` ` ` ` `9007199254740992 | 5 1 5 | ` | ` |
1:128 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 2^128 | 5 1 5 | ` | ` |
1:256 ` ` ` ` ` | ` ` ` ` ` ` ` ` ` ` 2^256 | 5 1 5 | ` | ` |
1:65536 ` ` ` ` | ` ` ` ` ` ` ` ` ` 2^65536 | 5 1 5 |16 |56 |
----------------+---------------------------+-------+---+---+---
1:2 2:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `36 | 5 2 2 | 1 | ` |
----------------+---------------------------+-------+---+---+---
2:1 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `15 | 5 2 3 | ` | ` |
1:2 3:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `20 | 5 2 3 | ` | ` |
2:1 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `21 | 5 2 3 | ` | ` |
1:3 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `24 | 5 2 3 | ` | ` |
1:1 6:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `26 | 5 2 3 | ` | ` |
1:2 4:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `28 | 5 2 3 | ` | ` |
1:1 9:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `46 | 5 2 3 | ` | ` |
1:4 2:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `48 | 5 2 3 | ` | ` |
1:1 3:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `50 | 5 2 3 | ` | ` |
1:1 2:3 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `54 | 5 2 3 | ` | ` |
1:1 4:2 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `98 | 5 2 3 | ` | ` |
1:1 2:4 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 162 | 5 2 3 |12 | ` |
----------------+---------------------------+-------+---+---+---
1:1 5:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `22 | 5 2 4 | ` | ` |
1:1 7:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `34 | 5 2 4 | ` | ` |
1:1 8:1 ` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` `38 | 5 2 4 | ` | ` |
1:1 16:1` ` ` ` | ` ` ` ` ` ` ` ` ` ` ` 106 | 5 2 4 | 4 |17 |73
================================================================
a = this sequence
g = rote weight in gammas = A062537
w = rote wayage in gammas = A001221
h = rote height in gammas = A109301
r = number in (g,h,w) set = A112481
s = count in (g, w) class = A111797
t = count in weight class = A061396

Links

Crossrefs

Cf. A000079, A001221, A007097, A014221, A050924.
Cf. A061396, A062504, A062537, A062860, A106177.
Cf. A109300, A109301, A111791 to A111800.
Cf. A112095, A112096, A112481.

A112481 Tetrahedron T(g, w, h) = number of rotes of weight g, wayage w, height h.

Original entry on oeis.org

1, 1, 2, 1, 4, 1, 8, 8, 2, 2, 12, 28, 16, 1, 12, 4
Offset: 1

Views

Author

Jon Awbrey, Sep 27 2005

Keywords

Comments

T(g, w, h) = |{m : A062537(m) = g, A001221(m) = w, A109301(m) = h}|.
This is the column that is labeled "r" in the tabulation of A112480.
a(n) is a permutation of the elements in A112096.
g = h > 0 implies w = 1 and T(j, 1, j) = 2^(j-1) = A000079(j-1).

Examples

			Table T(g, w, h), omitting empty cells, starts out as follows:
--------+-------------------------------------------------------
g\(w,h) | (0,0) (1,1) (1,2) ` ` ` (1,3) ` ` ` (1,4) ` ` ` (1,5)
` ` ` ` | ` ` ` ` ` ` ` ` ` (2,2) ` ` ` (2,3) ` ` ` (2,4) ` ` `
========+=======================================================
0 ` ` ` | ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
--------+-------------------------------------------------------
1 ` ` ` | ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
--------+-------------------------------------------------------
2 ` ` ` | ` ` ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
--------+-------------------------------------------------------
3 ` ` ` | ` ` ` ` ` ` ` 1 ` ` ` ` ` 4 ` ` ` ` ` ` ` ` ` ` ` ` `
3 ` ` ` | ` ` ` ` ` ` ` ` ` ` 1 ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `
--------+-------------------------------------------------------
4 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` ` 8 ` ` ` ` ` 8 ` ` ` ` ` ` `
4 ` ` ` | ` ` ` ` ` ` ` ` ` ` 2 ` ` ` ` ` 2 ` ` ` ` ` ` ` ` ` `
--------+-------------------------------------------------------
5 ` ` ` | ` ` ` ` ` ` ` ` ` ` ` ` `12 ` ` ` ` `28 ` ` ` ` `16 `
5 ` ` ` | ` ` ` ` ` ` ` ` ` ` 1 ` ` ` ` `12 ` ` ` ` ` 4 ` ` ` `
--------+-------------------------------------------------------
Row sums = A111797. Horizontal section sums = A061396.

Links

Crossrefs

Cf. A000079, A001221, A007097, A014221, A050924.
Cf. A061396, A062504, A062537, A062860, A106177.
Cf. A109300, A109301, A111791 to A111800.
Cf. A112095, A112096, A112480.
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