A148506 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, 0, 0), (-1, 1, 0), (1, -1, -1), (1, 0, 0)}.

1, 1, 3, 5, 17, 34, 121, 275, 1027, 2590, 10031, 27276, 108111, 309217, 1245407, 3700035, 15109579, 46351554, 191582849, 603772290, 2520070013, 8119770391, 34161939771, 112140631822, 475080016603, 1585016149409, 6756186193979, 22864248697362, 97983457230083, 335767435376344, 1445687258129657, 5009219815624807

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A151261 A148504 A148505 * A148507 A148508 A148509

Adjacent sequences: A148503 A148504 A148505 * A148507 A148508 A148509

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved