A150653 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, 0, 1), (0, 0, 1), (1, -1, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 28, 119, 525, 2372, 10913, 50838, 239117, 1132997, 5399870, 25858176, 124308107, 599535016, 2899495110, 14055672883, 68275267418, 332234541047, 1619209690761, 7902436162664, 38614800318249, 188897669705055, 924980643290845, 4533480169912369, 22237657521145814, 109162712586546648

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A161944 A150652 A130655 * A150654 A150655 A005436

Adjacent sequences: A150650 A150651 A150652 * A150654 A150655 A150656

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved