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A024394
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a(n) is the sum of squares of the first n positive integers congruent to 2 mod 3.
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1
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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
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OFFSET
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1,1
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COMMENTS
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Binomial transform of 0, 4, 21, 18, 0, 0, 0, 0, ...
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LINKS
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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).
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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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
(PARI) a(n) = 3*n^3+n*(3*n-1)/2; \\ Altug Alkan, Sep 20 2018
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CROSSREFS
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Sequence in context: A184301 A192025 A288542 * A199399 A211545 A295842
Adjacent sequences: A024391 A024392 A024393 * A024395 A024396 A024397
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KEYWORD
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nonn,easy
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AUTHOR
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Clark Kimberling
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STATUS
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approved
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