A150666 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, 0), (1, 0, 0), (1, 0, 1)}.

1, 2, 8, 24, 102, 353, 1587, 5924, 27262, 106387, 498123, 2005025, 9489971, 39050286, 186317796, 779778190, 3742856419, 15874268538, 76548900084, 328182985338, 1588477518666, 6871303138748, 33359323932901, 145393829934545, 707654381368129, 3104198520808458, 15140762252905112, 66788228762908015

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, 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: A060899 A213951 A150665 * A150667 A150668 A295583

Adjacent sequences: A150663 A150664 A150665 * A150667 A150668 A150669

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved