login
A150761
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, 0), (0, 0, -1), (0, 1, 1), (1, 0, 1)}
0
1, 2, 8, 30, 122, 522, 2256, 9962, 44796, 202794, 927606, 4280380, 19845134, 92551574, 433896100, 2040965858, 9637093830, 45662395760, 216890822656, 1032968093538, 4931746517340, 23590284027536, 113064621405454, 542898978102980, 2610696774382372, 12573536548269058, 60642739428964046
OFFSET
0,2
LINKS
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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A150760 A230588 A151303 * A373176 A150762 A074026
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved