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

Author

Clark Kimberling

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

Magma

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

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 *)

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

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