A149773 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), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 19, 77, 327, 1405, 6273, 28345, 128809, 594849, 2751489, 12860325, 60358301, 284534221, 1348008781, 6402370295, 30524174069, 145886185525, 698970734067, 3356852938895, 16150548427441, 77856997636305, 375909292937717, 1817768527185891, 8802335789589651, 42677575802561057, 207169189165130387

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, -1 + k, -1 + n] + aux[-1 + i, 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: A149771 A149772 A370194 * A363548 A149774 A160702

Adjacent sequences: A149770 A149771 A149772 * A149774 A149775 A149776

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved