A024215 Sum of squares of first n positive integers congruent to 1 mod 3.

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

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