A150092 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), (0, 0, 1), (1, 0, -1), (1, 0, 0)}.

1, 2, 6, 19, 66, 245, 948, 3791, 15476, 64402, 272700, 1171314, 5090997, 22334327, 98802899, 440488059, 1977476043, 8931332628, 40548362135, 184956945997, 847373416171, 3897973137387, 17996663755917, 83361921555277, 387303463238708, 1804529801429929, 8430001295617115, 39477866487103539

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, j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, 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: A150090 A150091 A190737 * A150093 A150094 A305118

Adjacent sequences: A150089 A150090 A150091 * A150093 A150094 A150095

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved