A148278 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), (-1, 1, 1), (1, -1, 1), (1, 0, 0)}.

1, 1, 2, 4, 15, 40, 166, 515, 2241, 7481, 33428, 117409, 534598, 1951131, 9007452, 33852509, 157910004, 607326940, 2855494418, 11189286399, 52936114932, 210652076234, 1001557345585, 4037507868399, 19275007001569, 78565275721462, 376348405678929, 1548720817943550, 7440216632167407

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[1 + 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: A148275 A148276 A148277 * A284728 A187928 A072206

Adjacent sequences: A148275 A148276 A148277 * A148279 A148280 A148281

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved