A150471 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, 0), (0, 0, -1), (0, 0, 1), (1, 1, 0)}.

1, 2, 7, 25, 99, 402, 1687, 7242, 31589, 139772, 625245, 2822337, 12844579, 58831382, 271083007, 1255384097, 5839684171, 27274710988, 127836802627, 601121704001, 2834831034433, 13404061945834, 63533284212965, 301801144126542, 1436577862779165, 6850988243782724, 32728987989031165, 156608974105107061

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, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A150468 A150469 A150470 * A150472 A150473 A150474

Adjacent sequences: A150468 A150469 A150470 * A150472 A150473 A150474

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved