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Number of perfect rhythmic tilings of [0,4n-1] with quadruplets.
7

%I #44 Mar 30 2021 14:27:31

%S 1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,2,2,24,38,96,444,1414,5134,19490

%N Number of perfect rhythmic tilings of [0,4n-1] with quadruplets.

%C A perfect tiling of the line with quadruplets consists of groups of four 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 Shalosh B. Ekhad, Lara Pudwell and Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/mamarim/mamarimhtml/johnson.html">A Perfect Rhythmic Tiling Of Quadruplets</a>, Nov. 30, 2004; <a href="/A261517/a261517.pdf">Local copy, pdf file only, no active links</a>

%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; <a href="/A261517/a261517_2.pdf">Local copy, pdf file only, no active links</a>

%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; <a href="/A261517/a261517_1.pdf">Local copy, pdf file only, no active links</a>

%e For n=1, there is 1 such tiling: (0,1,2,3).

%e For n=15, there are 2 such tilings: [0, 16, 32, 48], [1, 3, 5, 7], [2, 13, 24, 35], [4, 22, 40, 58], [6, 21, 36, 51], [8, 14, 20, 26], [9, 10, 11, 12], [15, 29, 43, 57], [17, 25, 33, 41], [18, 30, 42, 54], [19, 23, 27, 31], [28, 37, 46, 55], [34, 39, 44, 49], [38, 45, 52, 59], [47, 50, 53, 56] and its mirror (see Ekhad et al. link).

%Y Cf. A060963, A261516.

%K nonn,more

%O 0,16

%A _Michel Marcus_, Aug 23 2015

%E a(21)-a(23) from _Fausto A. C. Cariboni_, Mar 18 2017

%E a(0)=1 prepended by _Seiichi Manyama_, Feb 22 2020