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.

Showing 1-3 of 3 results.

A111797 Triangle T(g, w) = number of rotes of weight g and wayage w.

Original entry on oeis.org

1, 1, 2, 5, 1, 16, 4, 56, 17
Offset: 1

Views

Author

Jon Awbrey, Sep 01 2005

Keywords

Comments

T(g, w) = |{positive integers m : A062537(m) = g and A001221(m) = w}|.
Row sums = A061396. See A111796 for definitions and further details.

Examples

			Table T(g, w), omitting zeros, begins as follows:
g\w| 0 ` 1 ` 2 ` 3 ` 4 ` 5
---+-----------------------
`0 | 1
`1 | ` ` 1
`2 | ` ` 2
`3 | ` ` 5 ` 1
`4 | ` `16 ` 4
`5 | ` `56 `17

Links

Crossrefs

Cf. A001221, A061396, A062504, A062537, A062860.
Cf. A111796, A111798, A111800.

A111796 Positive integers sorted by rote weight (A062537) and omega (A001221).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 16, 6, 11, 13, 17, 19, 23, 25, 27, 32, 49, 53, 64, 81, 128, 256, 512, 65536, 10, 12, 14, 18
Offset: 1

Views

Author

Jon Awbrey, Sep 01 2005

Keywords

Comments

Positive integers m sorted by g(m) = A062537(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 Integers, Primal Codes, Sort Parameters and Subtotals
` ` a ` code` ` | g w | s | t
----------------+-----+---+---
` ` 1 = { } ` ` | 0 0 | 1 | 1
----------------+-----+---+---
` ` 2 = 1:1 ` ` | 1 1 | 1 | 1
----------------+-----+---+---
` ` 3 = 2:1 ` ` | 2 1 | ` |
` ` 4 = 1:2 ` ` | 2 1 | 2 | 2
----------------+-----+---+---
` ` 5 = 3:1 ` ` | 3 1 | ` |
` ` 7 = 4:1 ` ` | 3 1 | ` |
` ` 8 = 1:3 ` ` | 3 1 | ` |
` ` 9 = 2:2 ` ` | 3 1 | ` |
` `16 = 1:4 ` ` | 3 1 | 5 |
----------------+-----+---+---
` ` 6 = 1:1 2:1 | 3 2 | 1 | 6
----------------+-----+---+---
` `11 = 5:1 ` ` | 4 1 | ` |
` `13 = 6:1 ` ` | 4 1 | ` |
` `17 = 7:1 ` ` | 4 1 | ` |
` `19 = 8:1 ` ` | 4 1 | ` |
` `23 = 9:1 ` ` | 4 1 | ` |
` `25 = 3:2 ` ` | 4 1 | ` |
` `27 = 2:3 ` ` | 4 1 | ` |
` `32 = 1:5 ` ` | 4 1 | ` |
` `49 = 4:2 ` ` | 4 1 | ` |
` `53 = 16:1` ` | 4 1 | ` |
` `64 = 1:6 ` ` | 4 1 | ` |
` `81 = 2:4 ` ` | 4 1 | ` |
` 128 = 1:7 ` ` | 4 1 | ` |
` 256 = 1:8 ` ` | 4 1 | ` |
` 512 = 1:9 ` ` | 4 1 | ` |
65536 = 1:16` ` | 4 1 |16 |
----------------+-----+---+---
` `10 = 1:1 3:1 | 4 2 | ` |
` `12 = 1:2 2:1 | 4 2 | ` |
` `14 = 1:1 4:1 | 4 2 | ` |
` `18 = 1:1 2:2 | 4 2 | 4 |20
----------------+-----+---+---
a = this sequence
g = rote weight in gammas = A062537
w = rote wayage in gammas = A001221
s = count in (g, w) class = A111797
t = count in weight class = A061396

Links

Crossrefs

Cf. A001221, A061396, A062504, A062537, A062860.
Cf. A111797, A111798, A111800.

A111799 Triangle T(h, w) = number of rotes of height h and wayage w.

Original entry on oeis.org

1, 1, 3, 4, 77
Offset: 1

Views

Author

Jon Awbrey, Sep 01 2005 - Sep 02 2005

Keywords

Comments

T(h, w) = |{positive integers m : A109301(m) = h and A001221(m) = w}|.
Let c(h) = 1 for h = 0 and A050924(h) for h > 0. In other words, c(h) is the sequence [1, A050924] = [1,1,2,9,10^9, ...] that begins with 1 and continues with the terms of A050924. Then the number of nonzero entries in row h is c(h) and their sum is A109300(h). See A111798 for definitions and further details.

Examples

			Table T(h, w), omitting zeros, begins as follows:
h\w| 0 ` 1 ` 2 ` 3 ` 4 ` 5 ` 6 ` 7 ` 8 ` 9
---+---------------------------------------
`0 | 1
`1 | ` ` 1
`2 | ` ` 3 ` 4
`3 | ` `77 ` ? ` ? ` ? ` ? ` ? ` ? ` ? ` ?

Links

Crossrefs

Cf. A001221, A007097, A050924, A061396, A062504, A062537, A062860.
Cf. A109300, A109301, A111791, A111792, A111793, A111798, A111800.
Showing 1-3 of 3 results.

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