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A149516 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, 1, 1)}. 1
1, 1, 5, 11, 49, 157, 629, 2319, 9309, 36067, 146735, 583717, 2403149, 9754979, 40462171, 166354683, 695612827, 2888616957, 12146055243, 50820925053, 214800425487, 904468489247, 3837974122189, 16240475548249, 69171748577847, 293963559264191, 1255748732370767, 5355420642656009 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..100

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, -1 + 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: A142238 A149514 A149515 * A149517 A149518 A149519

Adjacent sequences:  A149513 A149514 A149515 * A149517 A149518 A149519

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified July 22 03:22 EDT 2017. Contains 289648 sequences.