OFFSET
1,2
COMMENTS
Arises in Routh's theorem.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
Eric Weisstein's World of Mathematics, Routh's Theorem.
Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).
FORMULA
G.f.: x*(1 + 7*x + 13*x^2 + 4*x^3 + 10*x^4 + 4*x^5 + x^6 + x^7 + x^8)/(1 - x^3)^3.
From Amiram Eldar, Aug 11 2022: (Start)
a(n) = numerator((n^2 + n + 1)/3).
Sum_{n>=1} 1/a(n) = (2*tanh(Pi/(2*sqrt(3))) + 3*tanh(sqrt(3)*Pi/2))*Pi/(3*sqrt(3)) - 1. (End)
MATHEMATICA
a[n_] := Denominator[(n - 1)^2/(n^2 + n + 1)]; Array[a, 50] (* Amiram Eldar, Aug 11 2022 *)
PROG
(Magma) [Denominator((n-1)^2/(n^2+n+1)): n in [1..70]]; // G. C. Greubel, Oct 27 2022
(SageMath) [denominator((n-1)^2/(n^2+n+1)) for n in range(1, 71)] # G. C. Greubel, Oct 27 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved