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A024215 Sum of squares of first n positive integers congruent to 1 mod 3. 4
1, 17, 66, 166, 335, 591, 952, 1436, 2061, 2845, 3806, 4962, 6331, 7931, 9780, 11896, 14297, 17001, 20026, 23390, 27111, 31207, 35696, 40596, 45925, 51701, 57942, 64666, 71891, 79635, 87916, 96752, 106161, 116161, 126770, 138006, 149887, 162431, 175656, 189580 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = n*(6*n^2 - 3*n - 1)/2.

G.f.: x*(1 + 13*x + 4*x^2) / (x-1)^4. - R. J. Mathar, Oct 08 2011

2*a(n) = A213826(n). - Clark Kimberling, Jul 04 2012

E.g.f.: (1/2)*(2*x + 15*x^2 + 6*x^3)*exp(x). - Franck Maminirina Ramaharo, Nov 23 2018

MATHEMATICA

a[n_] := n*(6*n^2 - 3*n - 1)/2; Array[a, 50] (* Amiram Eldar, Nov 23 2018 *)

Accumulate[Range[1, 202, 3]^2] (* Harvey P. Dale, Aug 24 2019 *)

PROG

(MAGMA) [n*(6*n^2-3*n-1)/2: n in [1..40]]; // Vincenzo Librandi, Oct 10 2011

(PARI) a(n)=n*(6*n^2-3*n-1)/2 \\ Charles R Greathouse IV, Oct 07 2015

(Sage) [n*(6*n^2-3*n-1)/2 for n in (1..40)] # G. C. Greubel, Nov 23 2018

CROSSREFS

Cf. A016777 (positive integers congruent to 1 mod 3).

Sequence in context: A065011 A031432 A157474 * A095071 A095072 A180529

Adjacent sequences:  A024212 A024213 A024214 * A024216 A024217 A024218

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified May 12 13:46 EDT 2021. Contains 343823 sequences. (Running on oeis4.)