A261516 Number of perfect rhythmic tilings of [0,3n-1] with triples.

1, 1, 0, 0, 0, 2, 0, 18, 66, 382, 1104, 4138, 15324, 61644, 325456, 2320948, 17660110, 148271962, 1171109228, 9257051746

Offset

0,6

Comments

A perfect tiling of the line with triples consists of groups of three evenly spaced points, each group having a different common interval such that all points of the line are covered.

References

J. P. Delahaye, La musique mathématique de Tom Johnson, in Mathématiques pour le plaisir, Belin-Pour la Science, Paris, 2010.

Links

Table of n, a(n) for n=0..19.

J. P. Delahaye, La musique mathématique de Tom Johnson, Pour la Science, 325, Nov 2004, pp. 88-93.

Tom Johnson, Perfect Rhythmic Tilings, Lecture delivered at MaMuX meeting, IRCAM, January 24, 2004.

Tom Johnson, Tiling in My music, August, 2008.

Example

For n=1, there is 1 such tiling: (0,1,2).
For n=5, there are 2 such tilings: (2,3,4), (8,10,12), (5,9,13), (1,6,11), (0,7,14) and its mirror, that have these distinct common differences: 1,2,4,5,7.

Crossrefs

Cf. A060963, A104429, A261517, A285527.

Sequence in context: A324665 A349036 A361591 * A009198 A209123 A139003

Adjacent sequences: A261513 A261514 A261515 * A261517 A261518 A261519

Keyword

nonn,more

Author

Michel Marcus, Aug 23 2015

Extensions

a(16)-a(17) from Alois P. Heinz, Sep 16 2015

a(18)-a(19) from Fausto A. C. Cariboni, Mar 27 2017

a(0)=1 prepended by Seiichi Manyama, Feb 21 2020

Status

approved