A149593 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, -1), (1, -1, -1), (1, 1, 1)}

1, 1, 5, 15, 57, 219, 923, 3835, 16373, 71049, 313877, 1397021, 6271765, 28362947, 129278243, 592589149, 2729588805, 12626351945, 58652928331, 273500977443, 1279554767405, 6003495416417, 28243174893659, 133208726181589, 629765157737029, 2983611472578201, 14162539037245515, 67348331991380805

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[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + 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: A149590 A149591 A149592 * A230986 A149594 A149595

Adjacent sequences: A149590 A149591 A149592 * A149594 A149595 A149596

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved