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A220443 a(n) = Sum_{i=1..n} (3i)^2. 1
0, 9, 45, 126, 270, 495, 819, 1260, 1836, 2565, 3465, 4554, 5850, 7371, 9135, 11160, 13464, 16065, 18981, 22230, 25830, 29799, 34155, 38916, 44100, 49725, 55809, 62370, 69426, 76995, 85095, 93744, 102960, 112761, 123165, 134190, 145854, 158175, 171171, 184860, 199260 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..40.

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

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = (3*n*(1+3*n+2*n^2))/2. G.f.: 9*x*(x+1) / (x-1)^4. - Colin Barker, Jul 22 2013

a(n) = A045943(n) * A005408(n). - Bruce J. Nicholson, Jun 12 2020

PROG

(PARI) a(n) = sum(k=1, n, (3*k)^2); \\ Michel Marcus, Aug 29 2015

CROSSREFS

Equals 9*A000330.

Cf. A045943, A005408.

Sequence in context: A068314 A152996 A188351 * A289721 A060008 A212089

Adjacent sequences:  A220440 A220441 A220442 * A220444 A220445 A220446

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Dec 22 2012

STATUS

approved

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Last modified July 24 06:04 EDT 2021. Contains 346273 sequences. (Running on oeis4.)