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 A080860 #28 Feb 15 2025 12:01:21
%S A080860 1,16,51,106,181,276,391,526,681,856,1051,1266,1501,1756,2031,2326,
%T A080860 2641,2976,3331,3706,4101,4516,4951,5406,5881,6376,6891,7426,7981,
%U A080860 8556,9151,9766,10401,11056,11731,12426,13141,13876,14631,15406,16201,17016,17851
%N A080860 a(n) = 10*n^2 + 5*n + 1.
%C A080860 The old definition of this sequence was "Generalized polygonal numbers".
%C A080860 Column T(n,5) of A080853.
%C A080860 Sequence found by reading the line from 1, in the direction 1, 16, ..., in the square spiral whose vertices are the generalized heptagonal numbers A085787. - _Omar E. Pol_, Sep 10 2011
%H A080860 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A080860 a(n) = C(5,0) + C(5,1)*n + C(5,2)*n^2.
%F A080860 G.f.: (C(4,0) + (C(6,2) - 2)*x + C(4,2)*x^2)/(1-x)^3 = (1 + 13*x + 6*x^2)/(1-x)^3.
%F A080860 a(n) = 20*n + a(n-1) - 5 with n > 0, a(0)=1. - _Vincenzo Librandi_, Aug 08 2010
%F A080860 From _Elmo R. Oliveira_, Oct 31 2024: (Start)
%F A080860 E.g.f.: exp(x)*(1 + 15*x + 10*x^2).
%F A080860 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%F A080860 Sum_{n>=0} a(n)/n! = 26*e. - _Davide Rotondo_, Feb 15 2025
%t A080860 Table[10n^2+5n+1,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{1,16,51},50] (* _Harvey P. Dale_, Aug 05 2014 *)
%o A080860 (PARI) a(n)=10*n^2+5*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A080860 Cf. A080853, A085787.
%K A080860 nonn,easy
%O A080860 0,2
%A A080860 _Paul Barry_, Feb 23 2003
%E A080860 Definition replaced with the closed form by _Bruno Berselli_, Jan 16 2013