A148129 - OEIS

A148129

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, 1), (-1, 0, 1), (-1, 1, -1), (0, 1, 0), (1, -1, 0)}.

1, 1, 2, 4, 11, 26, 75, 231, 714, 2253, 7439, 24739, 83518, 290505, 1020477, 3617151, 12988441, 47028018, 171707245, 633525246, 2353982342, 8798512258, 33091091756, 125118844853, 475659961733, 1818108173316, 6980593935149, 26910085515567, 104137310867262, 404464619751576, 1576642426385280

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..30.

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A148126 A148127 A148128 * A340651 A123432 A345216

Adjacent sequences: A148126 A148127 A148128 * A148130 A148131 A148132

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved