A149609 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), (1, -1, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 15, 63, 223, 1007, 3987, 17731, 72801, 332205, 1419247, 6445743, 27950963, 128654771, 569100817, 2614464453, 11656479779, 53994824919, 243589190703, 1127393066207, 5110585702669, 23786648346813, 108663988634677, 505588687584117, 2317135339756865, 10825211344617269, 49882062098721267

Offset

0,3

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 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: A191678 A149607 A149608 * A149610 A149611 A149612

Adjacent sequences: A149606 A149607 A149608 * A149610 A149611 A149612

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved