A149761 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), (-1, 0, 1), (0, -1, 1), (0, 0, -1), (1, 1, 1)}.

1, 1, 5, 19, 71, 289, 1223, 5203, 22415, 97869, 431155, 1911777, 8534569, 38305925, 172641851, 781231793, 3548304153, 16165900741, 73854023197, 338260967667, 1552835791277, 7143364707329, 32923999090571, 152014881331641, 703007464681223, 3255996384526583, 15101293781071973, 70130698637215877

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, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A083588 A149759 A149760 * A149762 A299107 A086386

Adjacent sequences: A149758 A149759 A149760 * A149762 A149763 A149764

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved