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 A226451 #19 Oct 15 2023 19:03:49
%S A226451 0,1,11,51,142,305,561,931,1436,2097,2935,3971,5226,6721,8477,10515,
%T A226451 12856,15521,18531,21907,25670,29841,34441,39491,45012,51025,57551,
%U A226451 64611,72226,80417,89205,98611,108656,119361,130747,142835,155646,169201,183521
%N A226451 a(n) = n*(7*n^2-12*n+7)/2.
%C A226451 See the comment in A226449.
%H A226451 Bruno Berselli, <a href="/A226451/b226451.txt">Table of n, a(n) for n = 0..1000</a>
%H A226451 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A226451 G.f.: x*(1+7*x+13*x^2)/(1-x)^4.
%F A226451 a(n) = A001106(n) + n*A001106(n-1).
%F A226451 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n >= 4. - _Wesley Ivan Hurt_, Oct 15 2023
%t A226451 Table[n (7 n^2 - 12 n + 7)/2, {n, 0, 40}]
%t A226451 CoefficientList[Series[x (1 + 7 x + 13 x^2)/(1 - x)^4, {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 18 2013 *)
%o A226451 (Magma) [n*(7*n^2-12*n+7)/2: n in [0..40]];
%o A226451 (Magma) I:=[0,1,11,51]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Aug 18 2013
%Y A226451 Cf. A001106.
%Y A226451 Similar sequences of the type b(m)+m*b(m-1), where b is a polygonal number: A006003, A069778, A143690, A204674, A212133, A226449, A226450.
%K A226451 nonn,easy
%O A226451 0,3
%A A226451 _Bruno Berselli_, Jun 07 2013