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A024394 a(n) is the sum of squares of the first n positive integers congruent to 2 mod 3. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Binomial transform of 0, 4, 21, 18, 0, 0, 0, 0, ...

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).

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

Adjacent sequences:  A024391 A024392 A024393 * A024395 A024396 A024397

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified August 7 12:01 EDT 2022. Contains 355985 sequences. (Running on oeis4.)