A149356 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, 0, 0), (-1, 0, 1), (0, -1, 0), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 43, 152, 609, 2346, 9645, 39039, 165579, 691291, 2982985, 12730758, 55745710, 241767355, 1069979231, 4698008068, 20974022559, 92994069426, 418085807507, 1868364801668, 8449111544666, 38004770958720, 172712042391537, 781132565846173, 3564796052139878, 16197957071972488

Offset

0,3

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A003444 A220881 A149355 * A149357 A149358 A149359

Adjacent sequences: A149353 A149354 A149355 * A149357 A149358 A149359

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved