A150670 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), (0, 0, -1), (0, 0, 1), (0, 1, -1), (1, 0, 1)}.

1, 2, 8, 25, 104, 391, 1666, 6881, 29855, 129545, 573055, 2554446, 11501808, 52133192, 238084704, 1092443168, 5042516850, 23364889005, 108739377523, 507833697775, 2379393048538, 11182563270522, 52693128537804, 248926453294921, 1178623958720194, 5592254793534124, 26586558799123717, 126622271913520750

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, j, -1 + k, -1 + n] + aux[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: A115256 A132963 A122404 * A150671 A150672 A150673

Adjacent sequences: A150667 A150668 A150669 * A150671 A150672 A150673

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved