A149129 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, -1, 0), (-1, 0, 0), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 9, 34, 105, 401, 1367, 5376, 19217, 77135, 286441, 1165086, 4445413, 18279080, 71040581, 294740394, 1162167377, 4855586573, 19378156339, 81423246854, 328163065039, 1385532042188, 5629572252919, 23866310197644, 97644986301889, 415416211191815, 1709825080248759, 7296401343604996

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 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: A149127 A163069 A149128 * A149130 A149131 A149132

Adjacent sequences: A149126 A149127 A149128 * A149130 A149131 A149132

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved