A149690 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, 0), (-1, 1, 1), (0, 0, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 67, 271, 1163, 4943, 21957, 97293, 437619, 1990411, 9106641, 41875849, 194172363, 903120009, 4218128269, 19796225031, 93155136939, 439615252675, 2081641739425, 9877145673315, 46968998112705, 223895477302189, 1069066983497841, 5113392368901125, 24502668424945695, 117574244770153825

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, j, 1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A149687 A149688 A149689 * A149691 A149692 A149693

Adjacent sequences: A149687 A149688 A149689 * A149691 A149692 A149693

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved