login
A149430
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), (0,1,-1), (1,1,1)}.
0
1, 1, 4, 13, 44, 160, 576, 2137, 8000, 30112, 114540, 436996, 1676116, 6453108, 24911776, 96460701, 374292952, 1455282884, 5668438104, 22111680424, 86375698280, 337822484240, 1322699806092, 5184073262824, 20336197487948, 79841329050480, 313699181900844, 1233386086431536, 4852469693781752
OFFSET
0,3
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, -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, 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: A149428 A149429 A045652 * A124463 A081197 A005490
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved