A150315 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, 1, 1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 21, 88, 307, 1373, 5156, 23729, 93107, 435598, 1760115, 8329158, 34383457, 164058562, 688393961, 3304773978, 14046675493, 67750533729, 290991214630, 1408760191081, 6103320310815, 29637576986412, 129344705240405, 629678677252834, 2765329194931020, 13490790506731302, 59569772001706791

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + 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: A150312 A150313 A150314 * A150316 A150317 A150318

Adjacent sequences: A150312 A150313 A150314 * A150316 A150317 A150318

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved