A149415 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, 0, 1), (-1, 1, 0), (1, 0, 1), (1, 1, -1)}

1, 1, 4, 12, 54, 184, 868, 3270, 15789, 62535, 305725, 1250467, 6158414, 25763798, 127467985, 542192997, 2690596202, 11591354117, 57638344104, 250831973091, 1249036545289, 5480410135621, 27317663458062, 120682044327008, 601992919806603, 2674803141963889, 13349816992232726, 59610044516852108

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A149413 A149414 A053454 * A149416 A149417 A151478

Adjacent sequences: A149412 A149413 A149414 * A149416 A149417 A149418

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved