A149476 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, 1, 1), (0, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 56, 226, 993, 4387, 19921, 91299, 424146, 1984585, 9359316, 44377511, 211482643, 1011882904, 4858879581, 23401436915, 113006754137, 546971963058, 2652858824592, 12889882826150, 62731663049380, 305741726340137, 1492077885605746, 7290260353306069, 35658493834967239, 174586407858085867

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, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A188205 A149474 A149475 * A121076 A121070 A163070

Adjacent sequences: A149473 A149474 A149475 * A149477 A149478 A149479

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved