A150896 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, 0, 1), (0, 1, 1), (1, -1, 1), (1, 1, -1), (1, 1, 0)}.

1, 2, 8, 34, 155, 726, 3473, 16808, 82057, 402924, 1986906, 9827983, 48725833, 241998673, 1203513633, 5991595084, 29853138232, 148839744996, 742458547822, 3705148091896, 18496276517214, 92359385390438, 461289973713636, 2304336348445719, 11512843889374112, 57527161714694147, 287480032036812539

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A235038 A150894 A150895 * A150897 A368763 A150898

Adjacent sequences: A150893 A150894 A150895 * A150897 A150898 A150899

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved