A024394 a(n) is the sum of squares of the first n positive integers congruent to 2 mod 3.
4, 29, 93, 214, 410, 699, 1099, 1628, 2304, 3145, 4169, 5394, 6838, 8519, 10455, 12664, 15164, 17973, 21109, 24590, 28434, 32659, 37283, 42324, 47800, 53729, 60129, 67018, 74414, 82335, 90799, 99824, 109428, 119629, 130445, 141894, 153994, 166763, 180219
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- D. Suprijanto, I. W. Suwarno, Observation on Sums of Powers of Integers Divisible by 3k-1, Applied Mathematical Sciences, Vol. 8, 2014, no. 45, pp. 2211-2217.
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
I:=[4, 29, 93, 214]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Jun 19 2012
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Mathematica
LinearRecurrence[{4,-6,4,-1},{4,29,93,214},40] (* Vincenzo Librandi, Jun 19 2012 *) Accumulate[Range[2,121,3]^2] (* Harvey P. Dale, Jun 24 2012 *) -
PARI
a(n) = 3*n^3+n*(3*n-1)/2; \\ Altug Alkan, Sep 20 2018
Formula
From R. J. Mathar, Oct 08 2011: (Start)
a(n) = 3*n^3 + 3*n^2/2 - n/2.
G.f.: x*(4 + 13*x + x^2) / (x-1)^4. (End)
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Vincenzo Librandi, Jun 19 2012
Comments