A150937 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), (0, 0, -1), (0, 1, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 34, 149, 655, 2973, 13542, 63195, 295239, 1391221, 6607775, 31486131, 150555115, 723726889, 3484954560, 16822569925, 81467300557, 395050078051, 1918852327159, 9340849113167, 45516027448659, 222061163876035, 1085070839303991, 5306236098700501, 25972730345997923, 127277059787467059

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A274750 A204444 A204430 * A150938 A151307 A150939

Adjacent sequences: A150934 A150935 A150936 * A150938 A150939 A150940

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved