A148798 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, 0), (0, -1, 1), (1, 0, -1), (1, 1, 0)}

1, 1, 3, 8, 25, 86, 278, 1008, 3689, 13682, 52296, 197227, 773129, 3046086, 12052354, 48408204, 193513935, 787775457, 3217911649, 13176702706, 54428194105, 224345229457, 934409171556, 3901537710521, 16317616662124, 68629517947273, 288349563162332, 1219663317366366, 5168604771907544

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A045900 A000738 A006372 * A148799 A148800 A244278

Adjacent sequences: A148795 A148796 A148797 * A148799 A148800 A148801

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved