A148100 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, 1), (0, -1, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 4, 10, 26, 76, 239, 753, 2540, 8572, 30128, 106501, 387844, 1422789, 5316121, 20099588, 76671429, 296355338, 1151184226, 4524804463, 17853802855, 71134139857, 284557313732, 1146559570375, 4641910594671, 18885060480277, 77240337339152, 316960064504831, 1307542974531887, 5407643110588584

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A000085 A222319 A047653 * A149815 A149816 A149817

Adjacent sequences: A148097 A148098 A148099 * A148101 A148102 A148103

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved