A150571 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), (0, 1, 1), (1, -1, 1), (1, 1, 0)}.

1, 2, 7, 26, 108, 453, 1991, 8790, 39647, 180294, 830133, 3845731, 17942624, 84128745, 396273416, 1873685843, 8891491081, 42325910206, 202038233279, 966747007053, 4635954881058, 22274520067968, 107215199263234, 516921586838909, 2496056612046261, 12069429770343532, 58434997240255297, 283249692910273673

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, 1 + j, -1 + k, -1 + n] + aux[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: A003447 A150569 A150570 * A150572 A150573 A150574

Adjacent sequences: A150568 A150569 A150570 * A150572 A150573 A150574

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved