A350384 a(n) = (-1728)^n.

1, -1728, 2985984, -5159780352, 8916100448256, -15407021574586368, 26623333280885243904, -46005119909369701466112, 79496847203390844133441536, -137370551967459378662586974208, 237376313799769806328950291431424, -410186270246002225336426103593500672

Offset: 0

Author

Stefano Spezia, Dec 28 2021

Keywords

• sign
• easy

Links

• Caroline Nunn, A Proof of a Generalization of Niven's Theorem Using Algebraic Number Theory, Rose-Hulman Undergraduate Mathematics Journal: Vol. 22, Iss. 2, Article 3 (2021).
• Index entries for linear recurrences with constant coefficients, signature (-1728).

Crossrefs

Cf. A000244, A000578, A001021, A008585, A008588, A262710.

Programs

Mathematica

LinearRecurrence[{-1728},{1},12]
NestList[-1728#&,1,20] (* Harvey P. Dale, Dec 25 2023 *)

Formula

From Caroline Nunn, p. 9: (Start)

a(n) = (3 + sqrt(-3))^(6*n).

a(n) = Sum_{k=0..3*n} (-1)^k*binomial(6*n, 2*k)*3^(6*n-k). (End)

O.g.f.: 1/(1 + 1728*x).

E.g.f.: exp(-1728*x).

a(n) = -1728*a(n-1) for n > 0.

a(n) = (-12)^(3*n).

a(n) = (A000244(n)*A262710(n))^3.