login
A150993
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, 1, -1), (1, 0, 1), (1, 1, 1)}.
0
1, 2, 9, 38, 168, 773, 3624, 17170, 82107, 395927, 1919236, 9343878, 45659222, 223779631, 1099440501, 5412768563, 26694974082, 131851281756, 652076574086, 3228477078910, 15999906011171, 79360689554108, 393929523637960, 1956676225180471, 9724648269216986, 48356574924226328, 240569126976728937
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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + 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: A037569 A291462 A001077 * A150994 A150995 A150996
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved