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A148462 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, 1, 0), (0, 0, 1), (1, -1, 0), (1, 1, -1)} 0
1, 1, 2, 6, 18, 61, 223, 835, 3296, 13280, 54828, 230937, 986261, 4275360, 18729877, 82912159, 370207793, 1665674199, 7546473001, 34395212088, 157636435318, 725993948563, 3358579055113, 15600331684473, 72730708595232, 340230220394416, 1596525730756138, 7513179574478844, 35450185529339379 (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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A192318 A192483 A150051 * A123639 A228448 A177473

Adjacent sequences:  A148459 A148460 A148461 * A148463 A148464 A148465

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified January 18 10:35 EST 2021. Contains 340254 sequences. (Running on oeis4.)