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 A080861 #22 Oct 21 2024 04:38:57
%S A080861 1,22,73,154,265,406,577,778,1009,1270,1561,1882,2233,2614,3025,3466,
%T A080861 3937,4438,4969,5530,6121,6742,7393,8074,8785,9526,10297,11098,11929,
%U A080861 12790,13681,14602,15553,16534,17545,18586,19657,20758,21889,23050,24241,25462,26713,27994
%N A080861 a(n) = 15*n^2 + 6*n + 1.
%C A080861 The old definition of this sequence was "Generalized polygonal numbers".
%C A080861 Column T(n,6) of A080853.
%H A080861 Vincenzo Librandi, <a href="/A080861/b080861.txt">Table of n, a(n) for n = 0..1000</a>
%H A080861 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A080861 a(n) = C(6,0) + C(6,1)*n + C(6,2)*n^2.
%F A080861 G.f.: (C(5,0) + (C(7,2)-2)*x + C(5,2)*x^2)/(1-x)^3 = (1 + 19*x + 10*x^2)/(1-x)^3.
%F A080861 From _Elmo R. Oliveira_, Oct 20 2024: (Start)
%F A080861 E.g.f.: exp(x)*(1 + 21*x + 15*x^2).
%F A080861 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A080861 CoefficientList[Series[(1 + 19 x + 10 x^2) / (1 - x)^3, {x, 0, 40}], x] (* _Vincenzo Librandi_, Aug 05 2013 *)
%t A080861 LinearRecurrence[{3, -3, 1}, {1, 22, 73}, 40] (* _Harvey P. Dale_, Sep 28 2019 *)
%o A080861 (Magma) [15*n^2 + 6*n + 1 : n in [0..40]]; // _Vincenzo Librandi_, Aug 05 2013
%o A080861 (PARI) a(n)=15*n^2+6*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A080861 Cf. A080853.
%K A080861 nonn,easy
%O A080861 0,2
%A A080861 _Paul Barry_, Feb 23 2003
%E A080861 Definition replaced with the closed form by _Bruno Berselli_, Jan 16 2013