A148733 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), (-1, 1, 0), (1, 0, -1), (1, 0, 1)}.

1, 1, 3, 7, 25, 77, 285, 913, 3701, 13063, 52643, 188689, 798789, 3006633, 12625037, 47906009, 207521071, 812293015, 3492286581, 13719773237, 60326990057, 242352250509, 1058223057199, 4256890213825, 18916952880911, 77415729873175, 341793832113371, 1398892954398399, 6265692614247403

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, j, 1 + k, -1 + n] + aux[1 + 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: A148732 A151269 A130463 * A148734 A124425 A321606

Adjacent sequences: A148730 A148731 A148732 * A148734 A148735 A148736

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved