A148568 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, 1, 0), (1, 0, -1), (1, 1, 0)}.

1, 1, 3, 6, 19, 48, 163, 458, 1623, 4873, 17694, 55688, 205205, 667727, 2489066, 8303744, 31230747, 106263877, 402383332, 1391009865, 5296310843, 18547893105, 70941590289, 251157988654, 964231083001, 3445375249027, 13269521569994, 47791310089513, 184566314074674, 669325853528842, 2590981483348106

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A226322 A148566 A148567 * A003162 A179277 A129417

Adjacent sequences: A148565 A148566 A148567 * A148569 A148570 A148571

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved