A150523 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, 1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 25, 104, 412, 1778, 7478, 32982, 142825, 639842, 2825774, 12772624, 57176195, 260372410, 1176668867, 5388408940, 24533970811, 112843715297, 516762635772, 2385717060932, 10976283769001, 50829743145803, 234764635020760, 1090040645670512, 5050745006814046, 23505242114690392, 109212324846740332

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, j, -1 + k, -1 + n] + aux[-1 + 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: A150520 A150521 A150522 * A150524 A150525 A150526

Adjacent sequences: A150520 A150521 A150522 * A150524 A150525 A150526

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved