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 1-2 of 2 results.

A128308 Binomial transform of A128307.

Original entry on oeis.org

1, 1, 1, 2, 2, 1, 6, 4, 3, 1, 19, 10, 7, 4, 1, 59, 29, 17, 11, 5, 1, 180, 88, 46, 28, 16, 6, 1, 544, 268, 134, 74, 44, 22, 7, 1, 1637, 812, 402, 208, 118, 66, 29, 8, 1, 4917, 2449, 1214, 610, 326, 184, 95, 37, 9, 1
Offset: 1

Views

Author

Gary W. Adamson, Feb 25 2007

Keywords

Comments

Row sums = A007051: (1, 2, 5, 14, 41, 122, ...).
See also the comments in A111277.

Examples

			First few rows of the triangle:
   1;
   1,  1;
   2,  2,  1;
   6,  4,  3,  1;
  19, 10,  7,  4,  1;
  59, 29, 17, 11,  5,  1;
  ...

Crossrefs

Cf. A007051, A128307, A007318.
The first column is A111277.

Formula

A007318 * A128307 as infinite lower triangular matrices.

Extensions

Crossref to A111277 added by Peter J. Taylor, Jul 23 2014

A244975 a(n) = (7^n - 2*n - 1)/4.

Original entry on oeis.org

0, 1, 11, 84, 598, 4199, 29409, 205882, 1441196, 10088397, 70618807, 494331680, 3460321794, 24222252595, 169555768205, 1186890377478, 8308232642392, 58157628496793, 407103399477603, 2849723796343276, 19948066574402990, 139636466020820991, 977455262145747001
Offset: 0

Views

Author

Vincenzo Librandi, Jul 09 2014

Keywords

Comments

This formula is considered in Theorem 5 of Shum's paper in References: on page 4 reads M(7^m,3) = (7^m - 2*m - 1)/4 for m >= 1, where M(r,s) is the number of the codewords in an optimal CAC(r,s), and CAC(r,s) denotes a conflict-avoiding codes of length r and weight s (see Introduction).

Links

Crossrefs

Cf. A000420, A005408, A111277, A135304.

Programs

  • Magma
    [(7^n-2*n-1)/4: n in [0..25]];
  • Mathematica
    Table[(7^n - 2 n - 1)/4, {n, 0, 30}] (* or *)
CoefficientList[Series[x (1 + 2 x)/((1 - 7 x) (1 - x)^2), {x, 0, 30}], x]

Formula

G.f.: x*(1+2*x)/((1-7*x)*(1-x)^2).
a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3). - Robert Israel, Jul 09 2014
From Elmo R. Oliveira, Apr 02 2025: (Start)
E.g.f.: exp(x)*(exp(6*x) - (2*x + 1))/4.
a(n) = (A000420(n) - A005408(n))/4. (End)

Extensions

Edited by Bruno Berselli, Jul 09 2014
Showing 1-2 of 2 results.

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