A148521 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), (1, -1, -1), (1, 1, 0)}.

1, 1, 3, 5, 17, 40, 133, 359, 1205, 3516, 12233, 37178, 130260, 409452, 1451523, 4699397, 16810715, 55338236, 199009269, 666159598, 2410618728, 8180797010, 29727470755, 101876698914, 371570011482, 1285650865868, 4705283364620, 16410476243304, 60221005216550, 211385681809822, 777637902953035, 2746296884209249

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[-1 + 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: A067062 A148519 A148520 * A303839 A148522 A308588

Adjacent sequences: A148518 A148519 A148520 * A148522 A148523 A148524

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved