A149488 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), (0, 1, 1), (1, -1, 0), (1, -1, 1), (1, 0, -1)}.

1, 1, 4, 14, 51, 201, 823, 3436, 14575, 62776, 273766, 1204282, 5337100, 23810913, 106823537, 481534000, 2179638646, 9902272921, 45133705547, 206310531515, 945515644303, 4343445670182, 19995082395510, 92225885065701, 426139227741927, 1972226545914777, 9141415516033028, 42429942858806258

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[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: A247415 A292463 A371870 * A058692 A165813 A253199

Adjacent sequences: A149485 A149486 A149487 * A149489 A149490 A149491

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved