A149200 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, 0, 1), (0, 1, -1), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 10, 38, 133, 512, 2022, 8128, 33730, 141324, 602890, 2601778, 11334514, 49900585, 221172359, 987885412, 4439103756, 20057110137, 91101700558, 415588883336, 1904000032055, 8755606765089, 40402666357108, 187042392647003, 868419079537612, 4043169630348568, 18871591885594103

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, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A149197 A149198 A149199 * A149201 A065524 A024689

Adjacent sequences: A149197 A149198 A149199 * A149201 A149202 A149203

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved