A150437 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), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 24, 100, 390, 1665, 7021, 30495, 132702, 586888, 2603104, 11643605, 52321106, 236264822, 1070743980, 4871310316, 22226431162, 101697222558, 466481434158, 2144573572559, 9879116930338, 45595011927220, 210793341152164, 976062088472396, 4526172443266586, 21017074534621855, 97713817319748696

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[i, -1 + j, -1 + 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: A197553 A213950 A123764 * A150438 A326336 A150439

Adjacent sequences: A150434 A150435 A150436 * A150438 A150439 A150440

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved