A324489 a(n) = A324488(n)/n.

1, 0, 21, 31, 266, 672, 3484, 11375, 48768, 177023, 716418, 2730315, 10878520, 42485638, 169181010, 670042125, 2678678730, 10705526976, 43007270292, 173003915322, 698235680844, 2822901487191, 11439823946306, 46438021798875, 188856966693230, 769224288476860, 3137871076604544, 12817404260955810

Offset

1,3

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.

Formula

From Seiichi Manyama, Apr 29 2021: (Start)

a(n) = (1/n) * Sum_{d|n} mu(n/d) * A001350(d)^3 = (1/n) * Sum_{d|n} mu(n/d) * A324487(d).

G.f.: Sum_{k>=1} mu(k) * log(f(x^k))/k , where f(x) = ((1-3*x+x^2) * (1+3*x+x^2))^3 * (1-x^2)^10/((1-4*x-x^2) * (1-x-x^2)^6 * (1+x-x^2)^9). (End)

Prog

(PARI) a001350(n) = fibonacci(n+1)+fibonacci(n-1)-1-(-1)^n;
a(n) = sumdiv(n, d, moebius(n/d)*a001350(d)^3)/n; \\ Seiichi Manyama, Apr 29 2021
(PARI) f(x) = ((1-3*x+x^2)*(1+3*x+x^2))^3*(1-x^2)^10/((1-4*x-x^2)*(1-x-x^2)^6*(1+x-x^2)^9);
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

Crossrefs

Cf. A060280, A324485, A324486, A324487, A324488.

Sequence in context: A106324 A208293 A032013 * A256824 A176558 A243360

Adjacent sequences: A324486 A324487 A324488 * A324490 A324491 A324492

Keyword

nonn

Author

N. J. A. Sloane, Mar 12 2019

Extensions

More terms from Seiichi Manyama, Apr 29 2021

Status

approved