login
A149868
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, 0), (-1, -1, 1), (0, 0, 1), (0, 1, -1), (1, 0, 0)}.
0
1, 2, 5, 13, 41, 139, 494, 1771, 6626, 25477, 99704, 394028, 1583784, 6453726, 26532762, 109902780, 459422070, 1935495454, 8199912534, 34928922249, 149648443966, 644305507731, 2785129360112, 12087444079695, 52667440706104, 230264645786360, 1009771676888315, 4441475020721976, 19591818756938375
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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A288388 A339224 A247981 * A343175 A007269 A179264
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved