A150721 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), (0, 0, 1), (1, 0, -1), (1, 1, 1)}.

1, 2, 8, 28, 118, 488, 2136, 9390, 42273, 191865, 881957, 4078484, 19000224, 88957680, 418583423, 1977346075, 9375000007, 44588517768, 212680559222, 1016991241328, 4874035721575, 23406774160600, 112615871664041, 542737149689428, 2619695685530567, 12662819055750401, 61288973817803354

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[i, j, -1 + 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: A151300 A150719 A150720 * A150722 A150723 A150724

Adjacent sequences: A150718 A150719 A150720 * A150722 A150723 A150724

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved