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A024394
a(n) is the sum of squares of the first n positive integers congruent to 2 mod 3.
2
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
1,1
COMMENTS
Binomial transform of 0, 4, 21, 18, 0, 0, 0, 0, ...
LINKS
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.
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
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 *)
PROG
(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
(PARI) a(n) = 3*n^3+n*(3*n-1)/2; \\ Altug Alkan, Sep 20 2018
CROSSREFS
Sequence in context: A184301 A192025 A288542 * A199399 A211545 A295842
KEYWORD
nonn,easy
STATUS
approved