%I
%S 1,1,0,0,0,0,0,0,0,18,40,66,0,0,0,0,0,0,400686,1738012,8495580,0,0,0,
%T 0,0,0
%N Number of super perfect rhythmic tilings of [0,3n1] with triples.
%C A super perfect tiling of the line with triples consists of n groups of three evenly spaced points, each group having a different common interval such that all points of the line are covered, and such that all intervals are inferior or equal to n (thus, each interval belongs to [1..n]).
%F For n>1, a(n) = A059108(n)*2 because A059108 ignores reflected solutions.  _Fausto A. C. Cariboni_, May 20 2017
%e For n = 9, there are 18 tilings.
%e One is: (0,2,4), (1,5,9), (3,11,19), (6,12,18), (7,14,21), (8,17,26), (10,13,16), (15,20,25), (22,23,24), with the intervals: 1,2,3,4,5,6,7,8,9 appearing in order: 2,4,8,6,7,9,3,5,1.
%e It can also be represented as:
%e 2 4 2 8 2 4 6 7 9 4 3 8 6 3 7 5 3 9 6 8 5 7 1 1 1 5 9
%Y Cf. A261516, A320392.
%K nonn,more
%O 0,10
%A _Tony Reix_, Apr 20 2017
