A148516 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, -1), (0, 0, 1), (0, 1, -1), (1, 0, -1)}.

1, 1, 3, 5, 17, 38, 135, 365, 1273, 3875, 13381, 44093, 153435, 529449, 1869835, 6615117, 23771839, 85625504, 312516149, 1142610611, 4216910530, 15617929355, 58165740582, 217808128603, 818152635521, 3089480284617, 11698729908551, 44468262860247, 169624275851796, 648612777109045, 2489332105439789

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, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A260406 A081762 A148515 * A148517 A148518 A077796

Adjacent sequences: A148513 A148514 A148515 * A148517 A148518 A148519

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved