A150534 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, 0), (-1, 1, 1), (1, 0, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 25, 110, 462, 2141, 9556, 45541, 210423, 1017684, 4801563, 23435336, 112095191, 550404475, 2657813608, 13104268115, 63714592627, 315077285841, 1539826890331, 7631392805453, 37442437107747, 185873645855999, 914767473468282, 4546966126158618, 22432315967942143, 111615010538402776

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A350796 A245157 A150533 * A150535 A076176 A188719

Adjacent sequences: A150531 A150532 A150533 * A150535 A150536 A150537

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved