A150547 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), (0, 1, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 26, 105, 426, 1823, 7779, 34008, 149349, 663184, 2958204, 13294636, 59928609, 271617284, 1234268264, 5629752155, 25739993324, 118012906757, 542163615314, 2496305115654, 11513424162006, 53198781619879, 246173784632759, 1140868462640989, 5294108372165852, 24598326710797491, 114422531344401338

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, -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: A150546 A151296 A141370 * A150548 A150549 A150550

Adjacent sequences: A150544 A150545 A150546 * A150548 A150549 A150550

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved