A220443 a(n) = Sum_{i=1..n} (3i)^2.

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

Offset: 0

Author

N. J. A. Sloane, Dec 22 2012

Keywords

• nonn
• easy

Links

• 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).

Crossrefs

Equals 9*A000330.

Cf. A045943, A005408.

Programs

PARI

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

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