A149170 - OEIS

A149170

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

1, 1, 4, 9, 44, 127, 619, 1989, 9856, 33919, 168677, 607001, 3024616, 11240063, 56097646, 213651441, 1066929850, 4142201763, 20695048729, 81607888787, 407840022294, 1629154166409, 8143064177452, 32884145423379, 164385396321806, 670058403611511, 3349805478222521, 13765134471463579

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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, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A284973 A239853 A209079 * A357447 A024053 A197970

Adjacent sequences: A149167 A149168 A149169 * A149171 A149172 A149173

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved