A150667 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, 0, 0), (-1, 1, 1), (1, 0, 0), (1, 0, 1)}.

1, 2, 8, 24, 104, 360, 1624, 6048, 27936, 108864, 510464, 2051456, 9719808, 39947648, 190710272, 797306880, 3828298240, 16222254080, 78243672064, 335196917760, 1622603599872, 7014447820800, 34056365273088, 148351482904576, 722064346365952, 3165937025024000, 15441892448436224, 68089360118611968

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, 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: A213951 A150665 A150666 * A150668 A295583 A150669

Adjacent sequences: A150664 A150665 A150666 * A150668 A150669 A150670

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved