A324485 a(n) = A324484(n)/n.

1, 0, 5, 6, 24, 40, 120, 250, 640, 1452, 3600, 8510, 20880, 50460, 124024, 303750, 750120, 1853120, 4600200, 11437548, 28527320, 71281800, 178526880, 447893250, 1125750120, 2833844040, 7144449920, 18036271740, 45591631800, 115381449692, 292329067800, 741410192250

Offset: 1

Author

N. J. A. Sloane, Mar 12 2019

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..2000
• M. Baake, J. Hermisson, and P. Pleasants, The torus parametrization of quasiperiodic LI-classes, J. Phys. A 30 (1997), no. 9, 3029-3056. See Table 4.

Crossrefs

Cf. A001350, A060280, A152152, A324483, A324484, A324489.

Programs

PARI

a001350(n) = fibonacci(n+1)+fibonacci(n-1)-1-(-1)^n;
a(n) = sumdiv(n, d, moebius(n/d)*a001350(d)^2)/n; \\ Seiichi Manyama, Apr 29 2021

PARI

f(x) = ((1-x-x^2)*(1+x-x^2))^2/((1-3*x+x^2)*(1-x)^2*(1+x)^4);
my(N=40, x='x+O('x^N)); Vec(sum(k=1, N, moebius(k)*log(f(x^k))/k)) \\ Seiichi Manyama, Apr 29 2021

Formula

From Seiichi Manyama, Apr 29 2021: (Start)

a(n) = (1/n) * Sum_{d|n} mu(n/d) * A001350(d)^2 = (1/n) * Sum_{d|n} mu(n/d) * A152152(d).

G.f.: Sum_{k>=1} mu(k) * log(f(x^k))/k , where f(x) = ((1-x-x^2) * (1+x-x^2))^2/((1-3*x+x^2) * (1-x)^2 * (1+x)^4). (End)

Extensions

More terms from Seiichi Manyama, Apr 29 2021