A148220 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, 0), (-1, 1, -1), (-1, 1, 0), (0, 1, 1), (1, -1, -1)}.

1, 1, 2, 4, 13, 31, 94, 288, 926, 2825, 9745, 32052, 109138, 371320, 1327340, 4545571, 16347289, 58255074, 211009754, 754764293, 2796072544, 10146730943, 37543834436, 138460496239, 518503084778, 1916205010224, 7232127953140, 27068784530059, 102332548484173, 385224642733386, 1469635346606949

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A148217 A148218 A148219 * A148221 A148222 A148223

Adjacent sequences: A148217 A148218 A148219 * A148221 A148222 A148223

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved