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 A080857 #27 May 07 2025 09:12:59
%S A080857 1,6,36,91,171,276,406,561,741,946,1176,1431,1711,2016,2346,2701,3081,
%T A080857 3486,3916,4371,4851,5356,5886,6441,7021,7626,8256,8911,9591,10296,
%U A080857 11026,11781,12561,13366,14196,15051,15931,16836,17766,18721,19701
%N A080857 a(n) = (25*n^2 - 15*n + 2)/2.
%C A080857 The old definition of this sequence was "Generalized polygonal numbers".
%C A080857 Row T(5,n) of A080853.
%C A080857 Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]=5, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n >= 3, a(n-1)=coeff(charpoly(A,x),x^(n-2)). - _Milan Janjic_, Jan 27 2010
%H A080857 Milan Janjić, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Janjic/janjic33.html">Hessenberg Matrices and Integer Sequences</a>, Journal of Integer Sequences, Vol. 13 (2010), Article 10.7.8.
%H A080857 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A080857 G.f.: (1+3*x+21*x^2)/(1-x)^3
%F A080857 a(n) = 25*n + a(n-1) - 20 with n > 0, a(0)=1. - _Vincenzo Librandi_, Aug 08 2010
%F A080857 From _Elmo R. Oliveira_, Oct 25 2024: (Start)
%F A080857 E.g.f.: exp(x)*(1 + 5*x + 25*x^2/2).
%F A080857 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A080857 Table[(25n^2-15n+2)/2,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{1,6,36},50] (* _Harvey P. Dale_, Aug 14 2018 *)
%o A080857 (PARI) a(n)=(25*n^2-15*n+2)/2 \\ _Charles R Greathouse IV_, Jun 17 2017
%K A080857 nonn,easy
%O A080857 0,2
%A A080857 _Paul Barry_, Feb 23 2003
%E A080857 Definition replaced with the closed form by _Bruno Berselli_, Jan 16 2013