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A150424 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), (0, 0, -1), (1, 0, 0), (1, 0, 1)} 0
1, 2, 7, 24, 96, 395, 1687, 7267, 32002, 142957, 647052, 2951242, 13554616, 62649395, 291367747, 1361774570, 6390662709, 30098529924, 142234054250, 674197080774, 3204389319941, 15266639069876, 72894588528203, 348761405871054, 1671733591940158, 8026757840934305, 38600359091389778, 185897884768617964 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[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: A005754 A007162 A150423 * A150425 A102286 A150426

Adjacent sequences: A150421 A150422 A150423 * A150425 A150426 A150427

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 29 14:48 EST 2022. Contains 358431 sequences. (Running on oeis4.)