A149553 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, 0), (-1, 1, 0), (1, -1, -1), (1, 1, 1)}

1, 1, 5, 13, 59, 187, 883, 3169, 14891, 55903, 267807, 1054621, 5047767, 20267863, 98066381, 404145263, 1954385933, 8141815955, 39645732343, 167944424539, 817364759403, 3486260053769, 17049299562711, 73581054318891, 359664099457269, 1559536855752195, 7650457837738635, 33467072828779151

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, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, 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: A084136 A091147 A351072 * A149554 A149555 A149556

Adjacent sequences: A149550 A149551 A149552 * A149554 A149555 A149556

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved