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A148569 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, 0, 0), (-1, 0, 1), (0, -1, 0), (0, 1, -1), (1, 0, 0)} 0
1, 1, 3, 6, 19, 51, 171, 529, 1873, 6282, 23178, 82111, 312399, 1151347, 4486888, 17037327, 67688801, 263109380, 1061979573, 4206602984, 17204567768, 69217318299, 286278353533, 1166888366939, 4872816562853, 20084030841891, 84572858282158, 351939906289740, 1492907600055839, 6264750054660970 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A179277 A129417 A132335 * A024998 A148570 A148571

Adjacent sequences:  A148566 A148567 A148568 * A148570 A148571 A148572

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified October 16 08:03 EDT 2018. Contains 316259 sequences. (Running on oeis4.)