OFFSET
1,1
LINKS
R. W. Hall and P. Klingsberg, Asymmetric Rhythms, Tiling Canons and Burnside's Lemma, Bridges Proceedings, pp. 189-194, 2004 (Winfield, Kansas).
R. W. Hall and P. Klingsberg, Asymmetric Rhythms and Tiling Canons, Preprint, 2004; The American Mathematical Monthly, Volume 113, 2006 - Issue 10, [alternative link].
FORMULA
a(n) = (Sum_{d|n}phi(3d) + Sum_{d|n, (3, d)=1}phi(d)*4^(n/d))/(3n), where phi(n) is the Euler function A000010.
a(n) ~ 4^n / (3*n). - Vaclav Kotesovec, Aug 28 2019
MATHEMATICA
a[n_] := (Sum[EulerPhi[3d], {d, Divisors[n]}] + Sum[Boole[CoprimeQ[3, d]] EulerPhi[d] 4^(n/d), {d, Divisors[n]}])/(3n);
Array[a, 25] (* Jean-François Alcover, Aug 28 2019 *)
PROG
(PARI) a(n) = (sumdiv(n, d, eulerphi(3*d)) + sumdiv(n, d, if (gcd(d, 3)==1, eulerphi(d)*4^(n/d))))/(3*n); \\ Michel Marcus, Aug 28 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Valery A. Liskovets, Jan 17 2006
STATUS
approved