A149377 - OEIS

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A149377

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, -1, 0), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 12, 48, 168, 734, 2901, 12956, 53952, 247794, 1076150, 5002284, 22265521, 104854868, 476333956, 2259433082, 10406933888, 49727145013, 231743193049, 1112557697545, 5229835292503, 25223740295131, 119457136172201, 578033615443152, 2753450989395258, 13365420050944659, 63989848689178980

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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[-1 + i, 1 + j, 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: A081620 A282023 A149376 * A063887 A149378 A149379

Adjacent sequences: A149374 A149375 A149376 * A149378 A149379 A149380

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved