A150668 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, 1), (-1, 1, 1), (1, 0, 0), (1, 1, 0)}.

1, 2, 8, 24, 110, 393, 1851, 7044, 34068, 136194, 662522, 2716549, 13350021, 56022703, 275842656, 1173650989, 5807929765, 25046792002, 124043751231, 539651966159, 2680235659308, 11763675559101, 58446599202430, 258096289547181, 1284576056431724, 5708047164923263, 28414745501331852, 126834039174077427

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, -1 + j, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150665 A150666 A150667 * A295583 A150669 A157005

Adjacent sequences: A150665 A150666 A150667 * A150669 A150670 A150671

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved