A148414 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, 0), (0, 1, 0), (1, -1, 1), (1, 0, -1)}.

1, 1, 2, 5, 17, 59, 216, 828, 3247, 13148, 54407, 229188, 980414, 4249191, 18618000, 82359851, 367516576, 1652036464, 7475296190, 34030364687, 155733266535, 716102735681, 3307436360573, 15335914559034, 71366807185820, 333228741232584, 1560640415079482, 7329647943131243, 34514759041244809

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A149997 A149998 A149999 * A306586 A232217 A150000

Adjacent sequences: A148411 A148412 A148413 * A148415 A148416 A148417

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved