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 A082041 #17 Oct 30 2024 16:02:51
%S A082041 1,21,73,157,273,421,601,813,1057,1333,1641,1981,2353,2757,3193,3661,
%T A082041 4161,4693,5257,5853,6481,7141,7833,8557,9313,10101,10921,11773,12657,
%U A082041 13573,14521,15501,16513,17557,18633,19741,20881,22053,23257,24493
%N A082041 a(n) = 16*n^2 + 4*n + 1.
%C A082041 Also sequence found by reading the segment (1,21) together with the line from 21, in the direction 21, 73, ..., in the square spiral whose vertices are the generalized decagonal numbers A074377. - _Omar E. Pol_, Nov 02 2012
%H A082041 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A082041 G.f.: (-1-18*x-13*x^2)/(x-1)^3 . - _R. J. Mathar_, Dec 03 2014
%F A082041 From _Elmo R. Oliveira_, Oct 28 2024: (Start)
%F A082041 E.g.f.: exp(x)*(1 + 20*x + 16*x^2).
%F A082041 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A082041 Table[16n^2+4n+1,{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{1,21,73},50] (* _Harvey P. Dale_, Sep 28 2024 *)
%o A082041 (PARI) a(n)=16*n^2+4*n+1 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y A082041 Column k=4 of A082039.
%Y A082041 Cf. A054569, A082040, A074377.
%K A082041 easy,nonn
%O A082041 0,2
%A A082041 _Paul Barry_, Apr 02 2003