A324488 Inflation orbit counts b^{(3)}_n for Danzer's F-type tiling and other 3D cut and project patterns with tau-inflation.

1, 0, 63, 124, 1330, 4032, 24388, 91000, 438912, 1770230, 7880598, 32763780, 141420760, 594798932, 2537715150, 10720674000, 45537538410, 192699485568, 817138135548, 3460078306440, 14662949297724, 62103832718202, 263115950765038, 1114512523173000, 4721424167330750

Offset: 1

Author

N. J. A. Sloane, Mar 12 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..1000
• M. Baake, J. Hermisson, and P. Pleasants, The torus parametrization of quasiperiodic LI-classes, J. Phys. A 30 (1997), no. 9, 3029-3056. See Tables 5 and 6.

Crossrefs

Cf. A001350, A031367, A324487, A324489.

Programs

PARI

a001350(n) = fibonacci(n+1)+fibonacci(n-1)-1-(-1)^n;
a(n) = sumdiv(n, d, moebius(n/d)*a001350(d)^3); \\ Seiichi Manyama, Apr 29 2021

Formula

a(n) = Sum_{d|n} mu(n/d) * A001350(d)^3 = Sum_{d|n} mu(n/d) * A324487(d). - Seiichi Manyama, Apr 29 2021

Extensions

More terms from Seiichi Manyama, Apr 29 2021