A150685 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, -1), (-1, 0, 1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 26, 116, 431, 2009, 7949, 37881, 155471, 750496, 3155109, 15356037, 65667616, 321397790, 1392068398, 6840459473, 29924242302, 147479673677, 650338251086, 3212391309294, 14258999189181, 70557681501725, 314918275880755, 1560500688513179, 6997721805028769, 34715071593120972, 156304645202393458

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A303478 A150683 A150684 * A150686 A150687 A150688

Adjacent sequences: A150682 A150683 A150684 * A150686 A150687 A150688

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved