A261517 Number of perfect rhythmic tilings of [0,4n-1] with quadruplets.

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

Offset: 0

Author

Michel Marcus, Aug 23 2015

Keywords

• nonn
• more

Comments

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.

Examples

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

References

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

Links

• J. P. Delahaye, La musique mathématique de Tom Johnson, Pour la Science, 325, Nov 2004, pp.88-93.
• Shalosh B. Ekhad, Lara Pudwell and Doron Zeilberger, A Perfect Rhythmic Tiling Of Quadruplets, Nov. 30, 2004; Local copy, pdf file only, no active links
• Tom Johnson, Perfect Rhythmic Tilings, Lecture delivered at MaMuX meeting, IRCAM, January 24, 2004; Local copy, pdf file only, no active links
• Tom Johnson, Tiling in My music, August, 2008; Local copy, pdf file only, no active links

Crossrefs

Cf. A060963, A261516.

Extensions

a(21)-a(23) from Fausto A. C. Cariboni, Mar 18 2017

a(0)=1 prepended by Seiichi Manyama, Feb 22 2020