A148010 - OEIS

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A148010

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

1, 1, 2, 3, 8, 15, 44, 101, 334, 817, 2752, 7084, 24607, 67680, 245864, 697772, 2553885, 7409054, 27480303, 82521955, 313794525, 959852546, 3664001178, 11345504079, 43619693769, 138028015239, 539448885144, 1727930112762, 6767820538432, 21845264940373, 85933511671898, 281615411418059, 1121090889944370

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..32.

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, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A148007 A148008 A148009 * A148011 A148012 A161178

Adjacent sequences: A148007 A148008 A148009 * A148011 A148012 A148013

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved