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A220442 a(n) = 3^n + 6^n + 9^n + 12^n. 1
4, 30, 270, 2700, 28674, 315900, 3564810, 40896900, 474714594, 5557298220, 65464673850, 774752404500, 9200707298514, 109548133495740, 1306873625950890, 15613382906014500, 186740100236842434, 2235305215228688460, 26773529476526331930, 320831460449198190900, 3845921314068458898354 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
T. A. Gulliver, Sums of Powers of Integers Divisible by Three, Int. J. Contemp. Math. Sciences, Vol. 7, 2012, no. 38, 1895 - 1901.
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 22 2012
STATUS
approved

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Last modified April 23 06:04 EDT 2024. Contains 371906 sequences. (Running on oeis4.)