A150128 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, 0, 0), (0, 0, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 20, 71, 270, 1059, 4287, 17778, 74969, 321429, 1394925, 6119233, 27101195, 120957641, 543776146, 2459693080, 11187357445, 51139563339, 234798585044, 1082437275132, 5008452007430, 23251728197988, 108280963715765, 505676245663004, 2367728191876043, 11113318374407351, 52279430267298249

Offset

0,2

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, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A301627 A163134 A370446 * A148480 A194950 A150129

Adjacent sequences: A150125 A150126 A150127 * A150129 A150130 A150131

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved