A149309 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, 1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 11, 48, 160, 736, 2661, 12446, 47969, 227591, 907792, 4352482, 17757644, 85648585, 356525315, 1728298464, 7296649603, 35514264747, 151581065164, 739817165935, 3189149570845, 15602739456306, 67789083839402, 332328271392838, 1453327449959479, 7135823916839902, 31393615362554965

Offset

0,3

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, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A149306 A149307 A149308 * A372115 A149310 A149311

Adjacent sequences: A149306 A149307 A149308 * A149310 A149311 A149312

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved