This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A062026 #24 Dec 07 2024 13:39:36
%S A062026 0,2,6,18,50,120,252,476,828,1350,2090,3102,4446,6188,8400,11160,
%T A062026 14552,18666,23598,29450,36330,44352,53636,64308,76500,90350,106002,
%U A062026 123606,143318,165300,189720,216752,246576,279378,315350,354690,397602,444296
%N A062026 a(n) = n*(n+1)*(n^2 - 3*n + 6)/4.
%C A062026 a(n) = 1*2*3 + 2*3*4 + 3*4*5 +. . .+ (n-2)*(n-1)*n +(n-1)*n*1+ n*1*2, the sum of the cyclic product of terms taken three at a time, final term being n*1*2=2n.
%H A062026 Harry J. Smith, <a href="/A062026/b062026.txt">Table of n, a(n) for n = 0..1000</a>
%H A062026 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A062026 a(n) = 2 * A004255(n).
%F A062026 a(0)=0, a(1)=2, a(2)=6, a(3)=18, a(4)=50, a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - _Harvey P. Dale_, Apr 22 2015
%F A062026 From _G. C. Greubel_, May 05 2022: (Start)
%F A062026 a(n) = 6*binomial(n+3, 4) - 12*binomial(n+2, 3) + 8*binomial(n+1, 2).
%F A062026 G.f.: 2*x*(1 - 2*x + 4*x^2)/(1-x)^5.
%F A062026 E.g.f.: (1/4)*x*(8 + 4*x + 4*x^2 + x^3)*exp(x). (End)
%e A062026 a(4) = 1*2*3 + 2*3*4 + 3*4*1 + 4*1*2 = 50.
%t A062026 Table[n(n+1)(n^2-3n+6)/4,{n,0,40}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{0,2,6,18,50},40] (* _Harvey P. Dale_, Apr 22 2015 *)
%o A062026 (PARI) a(n) = n*(n+1)*(n^2 -3*n +6)/4 \\ _Harry J. Smith_, Jul 29 2009
%o A062026 (SageMath) [n*(n+1)*(n^2-3*n+6)/4 for n in (0..40)] # _G. C. Greubel_, May 05 2022
%Y A062026 Cf. A004255.
%K A062026 nonn,easy
%O A062026 0,2
%A A062026 _Amarnath Murthy_, Jun 02 2001
%E A062026 More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001