A150444 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, 1, 0), (1, 0, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 24, 102, 411, 1835, 7893, 36351, 162548, 762138, 3491511, 16564826, 77136405, 369070850, 1739073648, 8372815451, 39802063614, 192546293264, 921550475054, 4474939591941, 21533004329067, 104880158196237, 506865300408766, 2474947871605487, 12003534219048160, 58733775050166893, 285703983345337690

Offset

0,2

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, j, k, -1 + n] + aux[1 + i, -1 + j, 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: A150442 A352906 A150443 * A150445 A150446 A150447

Adjacent sequences: A150441 A150442 A150443 * A150445 A150446 A150447

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved