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A131402 2*A007318 - (A046854 + A065941 - A000012). 3
1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 6, 7, 6, 1, 1, 7, 14, 14, 7, 1, 1, 9, 20, 33, 20, 9, 1, 1, 10, 31, 56, 56, 31, 10, 1, 1, 12, 40, 97, 111, 97, 40, 12, 1, 1, 13, 55, 142, 217, 217, 142, 55, 13, 1, 1, 15, 67, 213, 358, 463, 358, 213, 67, 15, 1, 1, 16, 86, 287, 590, 841, 841, 590, 287, 86, 16, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums = A131403: (1, 2, 5, 10, 21, 44, 93, ...).

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..1274

FORMULA

2*A007318 - (A046854 + A065941 - A000012) as infinite lower triangular matrices.

T(n,k) = 2*binomial(n, k) + 1 - binomial(floor(n + k)/2), k) - binomial(n-floor((k+1)/2), floor(k/2)). - Andrew Howroyd, Aug 09 2018

EXAMPLE

First few rows of the triangle are:

  1;

  1,  1;

  1,  3,  1;

  1,  4,  4,  1;

  1,  6,  7,  6,  1;

  1,  7, 14, 14,  7,  1;

  1,  9, 20, 33, 20,  9,  1;

  1, 10, 31, 56, 56, 31, 10,  1;

  ...

PROG

(PARI) T(n, k) = if(k <= n, 2*binomial(n, k) + 1 - binomial((n + k)\2, k) - binomial(n-(k+1)\2, k\2), 0) \\ Andrew Howroyd, Aug 09 2018

CROSSREFS

Row sums are A131403.

Cf. A046854, A065941.

Sequence in context: A013580 A147290 A026670 * A238498 A026626 A136482

Adjacent sequences:  A131399 A131400 A131401 * A131403 A131404 A131405

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jul 07 2007

EXTENSIONS

Missing terms inserted and a(55) and beyond from Andrew Howroyd, Aug 09 2018

STATUS

approved

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Last modified January 26 11:22 EST 2022. Contains 350598 sequences. (Running on oeis4.)