A148576 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, -1), (-1, 0, 1), (-1, 1, 0), (1, -1, 0), (1, 0, 0)}.

1, 1, 3, 6, 20, 50, 185, 518, 2030, 6148, 24846, 79517, 328434, 1093141, 4596452, 15762558, 67208043, 236101363, 1017431745, 3645586226, 15845246901, 57710489171, 252664692401, 932991093721, 4110109045187, 15357622575933, 68011015444863, 256752971116282, 1142179977377490, 4350908619896041

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A005558 A138350 A148575 * A148577 A148578 A182299

Adjacent sequences: A148573 A148574 A148575 * A148577 A148578 A148579

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved