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A149210 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, 0, 0), (0, 1, -1), (1, -1, 1), (1, 1, 0)} 0
1, 1, 4, 10, 40, 138, 551, 2157, 8810, 36647, 154078, 661375, 2854646, 12490169, 55043299, 244367746, 1093384878, 4915059946, 22237882646, 101035126126, 461173650726, 2113656372476, 9720476876090, 44867012962344, 207692597912237, 964303906233908, 4489064030758398, 20948595168627176 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..27.

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A149209 A053792 A032121 * A149211 A149212 A223160

Adjacent sequences:  A149207 A149208 A149209 * A149211 A149212 A149213

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified September 25 03:24 EDT 2020. Contains 337333 sequences. (Running on oeis4.)