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A149944 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), (0, 0, -1), (0, 1, 0), (1, 0, 1)} 0
1, 2, 5, 15, 50, 164, 556, 1940, 6933, 24744, 89546, 327038, 1207300, 4459302, 16591211, 61991530, 233069224, 876816387, 3313333609, 12551052159, 47736490574, 181653337777, 693339189471, 2650530514317, 10161297052095, 38971134119472, 149790839313023, 576374272138597, 2222447385907847 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, 1 + 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: A148366 A005751 A202182 * A149945 A149946 A149947

Adjacent sequences:  A149941 A149942 A149943 * A149945 A149946 A149947

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 29 09:16 EDT 2020. Contains 334697 sequences. (Running on oeis4.)