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A148675 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, 1, -1), (1, 0, -1), (1, 1, 0)} 0
1, 1, 3, 7, 21, 65, 205, 713, 2399, 8807, 31423, 118403, 442903, 1696475, 6569623, 25553523, 101307245, 400537565, 1612283869, 6479393097, 26354237909, 107481783441, 440881860189, 1819850183485, 7525644193561, 31351482619465, 130708930200313, 548353337148221, 2304188571803413 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + 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: A109361 A052805 A148674 * A148676 A105864 A130380

Adjacent sequences:  A148672 A148673 A148674 * A148676 A148677 A148678

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 31 09:30 EDT 2020. Contains 334748 sequences. (Running on oeis4.)