A149412 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, 1, 1), (0, 1, -1), (1, -1, 1), (1, 1, 0)}

1, 1, 4, 12, 52, 200, 906, 3835, 17835, 79215, 374381, 1710234, 8170299, 38011835, 182943410, 862048941, 4171224246, 19838535950, 96382566615, 461629848142, 2249821353330, 10834620431069, 52936934322254, 256041710688572, 1253562592466569, 6084551109301534, 29840382820005767, 145261082306545356

Offset

0,3

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A149409 A149410 A149411 * A259274 A109499 A282587

Adjacent sequences: A149409 A149410 A149411 * A149413 A149414 A149415

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved