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A151027 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), (1, 0, -1), (1, 0, 1), (1, 1, 1)} 0
1, 2, 10, 40, 196, 868, 4296, 19948, 99144, 470996, 2346544, 11302204, 56384200, 273994132, 1367983448, 6688214316, 33408923728, 164055354132, 819743599992, 4038463409468, 20183298573400, 99679703789508, 498243515811936, 2465452041200476, 12324560752499896, 61079384649652052, 305349388057227336 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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, 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: A151025 A030534 A151026 * A188325 A151028 A282619

Adjacent sequences:  A151024 A151025 A151026 * A151028 A151029 A151030

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 18 12:00 EDT 2019. Contains 327170 sequences. (Running on oeis4.)