A151114 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, -1), (0, 0, 1), (1, 0, 1), (1, 1, 0)}.

1, 3, 11, 45, 191, 847, 3822, 17578, 81724, 383678, 1814084, 8628020, 41233524, 197843539, 952505054, 4598984875, 22260818412, 107984125633, 524813929581, 2554935276695, 12456710528600, 60814480191677, 297257202483912, 1454551892016978, 7124492832319052, 34927596522506341, 171372158346393487

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, k, -1 + n] + aux[-1 + i, j, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A083324 A238578 A151113 * A083878 A363183 A151115

Adjacent sequences: A151111 A151112 A151113 * A151115 A151116 A151117

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved