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

%I A024215 #40 Sep 08 2022 08:44:48
%S A024215 1,17,66,166,335,591,952,1436,2061,2845,3806,4962,6331,7931,9780,
%T A024215 11896,14297,17001,20026,23390,27111,31207,35696,40596,45925,51701,
%U A024215 57942,64666,71891,79635,87916,96752,106161,116161,126770,138006,149887,162431,175656,189580
%N A024215 Sum of squares of first n positive integers congruent to 1 mod 3.
%H A024215 Vincenzo Librandi, <a href="/A024215/b024215.txt">Table of n, a(n) for n = 1..10000</a>
%H A024215 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A024215 a(n) = n*(6*n^2 - 3*n - 1)/2.
%F A024215 G.f.: x*(1 + 13*x + 4*x^2) / (x-1)^4. - _R. J. Mathar_, Oct 08 2011
%F A024215 2*a(n) = A213826(n). - _Clark Kimberling_, Jul 04 2012
%F A024215 E.g.f.: (1/2)*(2*x + 15*x^2 + 6*x^3)*exp(x). - _Franck Maminirina Ramaharo_, Nov 23 2018
%t A024215 a[n_] := n*(6*n^2 - 3*n - 1)/2; Array[a, 50] (* _Amiram Eldar_, Nov 23 2018 *)
%t A024215 Accumulate[Range[1,202,3]^2] (* _Harvey P. Dale_, Aug 24 2019 *)
%o A024215 (Magma) [n*(6*n^2-3*n-1)/2: n in [1..40]]; // _Vincenzo Librandi_, Oct 10 2011
%o A024215 (PARI) a(n)=n*(6*n^2-3*n-1)/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A024215 (Sage) [n*(6*n^2-3*n-1)/2 for n in (1..40)] # _G. C. Greubel_, Nov 23 2018
%Y A024215 Cf. A016777 (positive integers congruent to 1 mod 3).
%K A024215 nonn,easy
%O A024215 1,2
%A A024215 _Clark Kimberling_