A150497 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, 1, -1), (0, 1, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 7, 25, 101, 408, 1723, 7314, 31715, 138570, 612009, 2720079, 12167213, 54695380, 247025885, 1119992583, 5095775185, 23254904456, 106415683613, 488163587257, 2244391150287, 10339826341516, 47723549083465, 220641597892882, 1021697042715601, 4737904273768066, 22000612630988067, 102288320698230433

Offset

0,2

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A150494 A150495 A150496 * A150498 A150499 A150500

Adjacent sequences: A150494 A150495 A150496 * A150498 A150499 A150500

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved