A150465 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, 0), (0, -1, 0), (0, 1, 1), (1, 1, 0)}.

1, 2, 7, 25, 98, 384, 1597, 6670, 28408, 122197, 532921, 2337294, 10329095, 45940042, 205457964, 922539912, 4160226856, 18832804377, 85520622884, 389438385157, 1778378619115, 8140951032081, 37345967380943, 171669588822748, 790652967249590, 3647705679269181, 16855138367966224, 78001628458109711

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, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A150462 A150463 A150464 * A150466 A150467 A150468

Adjacent sequences: A150462 A150463 A150464 * A150466 A150467 A150468

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved