A149675 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, 1), (0, 0, -1), (1, -1, 0), (1, 1, 1)}.

1, 1, 5, 17, 65, 261, 1085, 4571, 19587, 84885, 371691, 1640097, 7286299, 32554855, 146180405, 659196933, 2984034309, 13553661103, 61747484695, 282070090245, 1291711612597, 5928513573073, 27265526668561, 125631143092757, 579873415046605, 2680800605312565, 12411974059778039, 57546369699984959

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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A046231 A092896 A149674 * A149676 A149677 A273856

Adjacent sequences: A149672 A149673 A149674 * A149676 A149677 A149678

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved