A150749 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, 1, 1), (1, -1, 0), (1, 1, 1)}

1, 2, 8, 29, 127, 526, 2420, 10624, 49846, 226007, 1074831, 4975408, 23852322, 111962249, 540110364, 2561114007, 12409220893, 59286982781, 288292731330, 1385471572325, 6755689212401, 32616834914307, 159413239163978, 772560860522906, 3782992084218568, 18390147847296445, 90197700595782482

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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + 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: A150746 A150747 A150748 * A150750 A150751 A150752

Adjacent sequences: A150746 A150747 A150748 * A150750 A150751 A150752

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved