A150447 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, -1), (0, 1, 1), (1, -1, 0), (1, 1, 0)}.

1, 2, 7, 24, 103, 410, 1847, 7940, 36766, 163895, 772073, 3533351, 16809456, 78212465, 375223703, 1766948740, 8522900287, 40504133663, 196267581473, 939071884790, 4566201223271, 21969474611050, 107126180830412, 517658720866700, 2530136067000315, 12270561599283960, 60089250242273967, 292289694151777174

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, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A150444 A150445 A150446 * A150448 A256492 A150449

Adjacent sequences: A150444 A150445 A150446 * A150448 A150449 A150450

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved