A148091 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, 1), (-1, 1, 1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 4, 10, 24, 75, 216, 714, 2207, 7436, 24191, 86048, 293747, 1067294, 3730715, 13746151, 49287908, 185552315, 679296274, 2582590609, 9579477462, 36808351636, 138548906824, 538038570723, 2047494127395, 8001858907158, 30725643664976, 120983795801398, 468789378026079, 1857083738842685

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A061055 A060776 A148090 * A123420 A000458 A089928

Adjacent sequences: A148088 A148089 A148090 * A148092 A148093 A148094

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved