A285527 Number of super perfect rhythmic tilings of [0,3n-1] with triples.

1, 1, 0, 0, 0, 0, 0, 0, 0, 18, 40, 66, 0, 0, 0, 0, 0, 0, 400686, 1738012, 8495580, 0, 0, 0, 0, 0, 0

Offset: 0

Author

Tony Reix, Apr 20 2017

Keywords

• nonn
• more

Comments

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]).

Examples

			For n = 9, there are 18 tilings.
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.
It can also be represented as:
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
		

Crossrefs

Cf. A261516, A320392.

Formula

For n>1, a(n) = A059108(n)*2 because A059108 ignores reflected solutions. - Fausto A. C. Cariboni, May 20 2017