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A148175 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, 1), (-1, 1, 0), (0, 1, 0), (1, -1, 0)} 0
1, 1, 2, 4, 12, 28, 86, 228, 764, 2154, 7536, 22483, 81267, 252254, 932906, 2985042, 11232797, 36792087, 140518797, 469089364, 1814209956, 6155398969, 24055291339, 82766261243, 326229083082, 1135997374249, 4510041959975, 15867458981614, 63395729623779, 225049801599639, 904250812480564, 3235644640583178 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..31.

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[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A096581 A275434 A151258 * A148176 A148177 A080876

Adjacent sequences:  A148172 A148173 A148174 * A148176 A148177 A148178

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified November 29 13:17 EST 2021. Contains 349416 sequences. (Running on oeis4.)