A148549 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, 0), (-1, 1, 1), (1, 0, 0)}.

1, 1, 3, 5, 21, 44, 179, 405, 1863, 4574, 20253, 51083, 242478, 638910, 2935563, 7830889, 37719955, 103473882, 485025311, 1338989811, 6504657404, 18317722002, 86944436845, 245672670625, 1200013129349, 3442388805084, 16479191579014, 47355255312875, 232190760680298, 675289949920232, 3252682484365329

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A096729 A001775 A148548 * A148550 A148551 A148552

Adjacent sequences: A148546 A148547 A148548 * A148550 A148551 A148552

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved