A150636 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), (0, 1, 1), (1, -1, 1), (1, 0, 0)}.

1, 2, 7, 27, 115, 510, 2328, 10833, 51111, 243674, 1171029, 5662910, 27521695, 134294202, 657460273, 3227490486, 15879933263, 78282626958, 386535501072, 1911253113840, 9461664131954, 46888603412740, 232572832029069, 1154498259011044, 5734934040381157, 28505510877536098, 141763357903663258

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, j, k, -1 + n] + aux[-1 + i, 1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A150633 A150634 A150635 * A084206 A150637 A150638

Adjacent sequences: A150633 A150634 A150635 * A150637 A150638 A150639

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved