A151111 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), (0, 1, 0), (1, 0, 0), (1, 1, 1)}.

1, 3, 11, 45, 187, 821, 3655, 16563, 76299, 353565, 1656135, 7795435, 36891565, 175420449, 836797617, 4006135089, 19230908851, 92540054469, 446356079927, 2156844527511, 10441603416177, 50626840016573, 245823100672597, 1195188859800625, 5817880545154171, 28351170944975535, 138298991887389517

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[i, -1 + j, 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: A369839 A151109 A151110 * A292278 A151112 A083324

Adjacent sequences: A151108 A151109 A151110 * A151112 A151113 A151114

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved