A150852 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, 0), (0, -1, 1), (1, 0, 1), (1, 1, -1), (1, 1, 0)}.

1, 2, 8, 32, 140, 628, 2887, 13510, 63956, 305600, 1471081, 7120355, 34625821, 169011611, 827494683, 4062062757, 19983319943, 98490098421, 486190982884, 2403321492423, 11894085670659, 58924714771134, 292183102398301, 1449964171395540, 7200509777155409, 35779851763911854, 177890764792584154

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150850 A179469 A150851 * A150853 A150854 A150855

Adjacent sequences: A150849 A150850 A150851 * A150853 A150854 A150855

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved