A220442 a(n) = 3^n + 6^n + 9^n + 12^n.

4, 30, 270, 2700, 28674, 315900, 3564810, 40896900, 474714594, 5557298220, 65464673850, 774752404500, 9200707298514, 109548133495740, 1306873625950890, 15613382906014500, 186740100236842434, 2235305215228688460, 26773529476526331930, 320831460449198190900, 3845921314068458898354

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

T. A. Gulliver, Sums of Powers of Integers Divisible by Three, Int. J. Contemp. Math. Sciences, Vol. 7, 2012, no. 38, 1895 - 1901.

Index entries for linear recurrences with constant coefficients, signature (30,-315,1350,-1944).

Formula

a(n) = 3^n*(2^n + 3^n + 4^n + 1).

G.f.: -2*(15*x-2)*(45*x^2-15*x+1) / ((3*x-1)*(6*x-1)*(9*x-1)*(12*x-1)). - Colin Barker, Jul 22 2013

Mathematica

Total/@Table[(3*Range[4])^n, {n, 0, 20}] (* or *) LinearRecurrence[ {30, -315, 1350, -1944}, {4, 30, 270, 2700}, 30] (* Harvey P. Dale, Jul 19 2014 *)
CoefficientList[Series[-2 (15 x - 2) (45 x^2 - 15 x + 1)/((3 x - 1) (6 x - 1) (9 x - 1) (12 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 22 2014 *)

Prog

(Python)
def a(n): return 3**n + 6**n + 9**n + 12**n
print([a(n) for n in range(21)]) # Michael S. Branicky, Apr 30 2021

Crossrefs

Sequence in context: A330801 A052658 A340895 * A215698 A367872 A179540

Adjacent sequences: A220439 A220440 A220441 * A220443 A220444 A220445

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 22 2012

Status

approved