A275635 a(n) = (3^n-1)*(3^n-3)*(3^n+3)/4!.

0, 0, 24, 780, 21840, 595320, 16120104, 435647940, 11766101280, 317717078640, 8578651865784, 231626215995900, 6253931369278320, 168856358797449960, 4559123593944869064, 123096354194148852660, 3323601717660497232960, 89737247766598954349280, 2422905702206059204441944

Offset

0,3

References

Turner, Zachary J., Bryson W. Finklea, and Terri Moore. "Combinatorial Approaches to Minimal Zero Sequences of Finite Abelian Groups, and a Surprising Connection." Preprint, Jan 09 2004.

Links

Colin Barker, Table of n, a(n) for n = 0..650

Index entries for linear recurrences with constant coefficients, signature (40,-390,1080,-729).

Formula

From Chai Wah Wu, Aug 09 2016: (Start)

a(n) = 40*a(n-1) - 390*a(n-2) + 1080*a(n-3) - 729*a(n-4) for n > 3.

G.f.: x^2*(-180*x + 24)/((x - 1)*(3*x - 1)*(9*x - 1)*(27*x - 1)). (End)

a(n) = (9-3^(2+n)-9^n+27^n)/24. - Colin Barker, Aug 10 2016

Mathematica

Table[(3^n - 1) (3^n - 3) (3^n + 3)/4!, {n, 0, 18}] (* or *)
CoefficientList[Series[x^2 (-180 x + 24)/((x - 1) (3 x - 1) (9 x - 1) (27 x - 1)), {x, 0, 18}], x] (* Michael De Vlieger, Aug 11 2016 *)
Table[(Times@@(3^n+{-3, -1, 3}))/24, {n, 0, 20}] (* or *) LinearRecurrence[{40, -390, 1080, -729}, {0, 0, 24, 780}, 20] (* Harvey P. Dale, Dec 11 2022 *)

Crossrefs

Sequence in context: A269147 A269209 A270252 * A158651 A265884 A204559

Adjacent sequences: A275632 A275633 A275634 * A275636 A275637 A275638

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 09 2016

Status

approved