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A167763 Pendular triangle (p=0), read by rows, where row n is formed from row n-1 by the recurrence: if n > 2k, T(n,k) = T(n,n-k) + T(n-1,k), otherwise T(n,k) = T(n,n-1-k) + p*T(n-1,k), for n >= k <= 0, with T(n,0)=1 and T(n,n)=0^n. 1
1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 3, 3, 1, 0, 1, 4, 7, 4, 1, 0, 1, 5, 12, 12, 5, 1, 0, 1, 6, 18, 30, 18, 6, 1, 0, 1, 7, 25, 55, 55, 25, 7, 1, 0, 1, 8, 33, 88, 143, 88, 33, 8, 1, 0, 1, 9, 42, 130, 273, 273, 130, 42, 9, 1, 0, 1, 10, 52, 182, 455, 728, 455, 182, 52, 10, 1, 0, 1, 11, 63, 245, 700 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

See A118340 for definition of pendular triangles and pendular sums.

LINKS

Table of n, a(n) for n=0..82.

FORMULA

T(2n+m) = [A001764^(m+1)](n), i.e., the m-th lower semi-diagonal forms the self-convolution (m+1)-power of A001764.

If n > 2k, T(n,k) = binomial(n+k+1,k)*(n-2k+1)/(n+k+1), else T(n,k) = T(n,n-1-k), with conditions: T(n,0)=1 for n>=0 and T(n,n)=0 for n > 0. - Paul D. Hanna, Nov 12 2009

EXAMPLE

Triangle begins:

  1;

  1,  0;

  1,  1,  0;

  1,  2,  1,  0;

  1,  3,  3,  1,  0;

  1,  4,  7,  4,  1,  0;

  1,  5, 12, 12,  5,  1,  0; ...

PROG

(PARI) {T(n, k)=if(k==0, 1, if(n==k, 0, if(n>2*k, binomial(n+k+1, k)*(n-2*k+1)/(n+k+1), T(n, n-1-k))))} \\ Paul D. Hanna, Nov 12 2009

CROSSREFS

Cf. A118340 for p=1, A118345 for p=2, A118350 for p=3.

Cf. A001764, A006013, A006629, A102893.

Sequence in context: A110555 A097805 A071919 * A277666 A274581 A247919

Adjacent sequences:  A167760 A167761 A167762 * A167764 A167765 A167766

KEYWORD

nonn,tabl

AUTHOR

Philippe Deléham, Nov 11 2009

STATUS

approved

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Last modified October 19 02:23 EDT 2018. Contains 316327 sequences. (Running on oeis4.)