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%I #47 Feb 22 2020 08:29:23
%S 1,1,0,0,0,2,0,18,66,382,1104,4138,15324,61644,325456,2320948,
%T 17660110,148271962,1171109228,9257051746
%N Number of perfect rhythmic tilings of [0,3n-1] with triples.
%C 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.
%D J. P. Delahaye, La musique mathématique de Tom Johnson, in Mathématiques pour le plaisir, Belin-Pour la Science, Paris, 2010.
%H J. P. Delahaye, <a href="http://www.pourlascience.fr/ewb_pages/a/article-la-musique-mathematique-de-tom-johnson-21813.php">La musique mathématique de Tom Johnson</a>, Pour la Science, 325, Nov 2004, pp. 88-93.
%H Tom Johnson, <a href="http://recherche.ircam.fr/equipes/repmus/mamux/documents/Perfectrhythmictilings.html">Perfect Rhythmic Tilings</a>, Lecture delivered at MaMuX meeting, IRCAM, January 24, 2004.
%H Tom Johnson, <a href="http://web.archive.org/web/20180504223959/http://editions75.com/Articles/Tiling%20in%20my%20music.pdf">Tiling in My music</a>, August, 2008.
%e For n=1, there is 1 such tiling: (0,1,2).
%e 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.
%Y Cf. A060963, A104429, A261517, A285527.
%K nonn,more
%O 0,6
%A _Michel Marcus_, Aug 23 2015
%E a(16)-a(17) from _Alois P. Heinz_, Sep 16 2015
%E a(18)-a(19) from _Fausto A. C. Cariboni_, Mar 27 2017
%E a(0)=1 prepended by _Seiichi Manyama_, Feb 21 2020
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