A150298 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, 1), (-1, 1, 1), (0, 1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 6, 23, 97, 422, 1894, 8633, 39881, 186176, 876243, 4151145, 19773413, 94604441, 454324159, 2188713679, 10572670774, 51191032546, 248363563505, 1207144727178, 5876520150690, 28648100639109, 139837347413001, 683358089728405, 3342912177491576, 16368649806541834, 80218953329000500

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A111283 A150297 A374165 * A280768 A370183 A278301

Adjacent sequences: A150295 A150296 A150297 * A150299 A150300 A150301

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved