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A149541 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, -1, 1), (-1, 0, -1), (1, 0, -1), (1, 1, 1)} 0
1, 1, 5, 13, 53, 181, 797, 2903, 12859, 50331, 225839, 906225, 4129853, 17040887, 77913159, 326996909, 1510147553, 6422569359, 29747117651, 128073608665, 596327616089, 2588195705585, 12089363646993, 52920358776527, 247883718872023, 1091627109014907, 5127795371773655, 22715769475682537 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

MATHEMATICA

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A007231 A158345 A149540 * A149542 A089794 A216821

Adjacent sequences:  A149538 A149539 A149540 * A149542 A149543 A149544

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified February 19 18:30 EST 2019. Contains 320327 sequences. (Running on oeis4.)