A148639 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, 0), (-1, 1, 1), (0, 0, -1), (1, 0, 0)}.

1, 1, 3, 6, 22, 62, 215, 692, 2458, 8708, 31475, 114824, 425486, 1599203, 6066110, 23109793, 88859981, 343913830, 1341472353, 5251722971, 20653709763, 81624357922, 324060423282, 1291616430745, 5162528072143, 20701942480772, 83287365946070, 336085597908264, 1359574925830446, 5512125864875680

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A148636 A148637 A148638 * A148640 A148641 A148642

Adjacent sequences: A148636 A148637 A148638 * A148640 A148641 A148642

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved