

A261516


Number of perfect rhythmic tilings of [0,3n1] with triples.


4



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

1,5


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, BelinPour la Science, Paris, 2010.


LINKS

Table of n, a(n) for n=1..19.
J. P. Delahaye, La musique mathématique de Tom Johnson, Pour la Science, 325, Nov 2004, pp. 8893.
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: (3,4,5), (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: A242569 A152154 A324665 * 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


STATUS

approved



