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 A202141 #27 Aug 23 2025 15:51:38
%S A202141 5,2,25,74,149,250,377,530,709,914,1145,1402,1685,1994,2329,2690,3077,
%T A202141 3490,3929,4394,4885,5402,5945,6514,7109,7730,8377,9050,9749,10474,
%U A202141 11225,12002,12805,13634,14489,15370,16277,17210,18169,19154,20165,21202,22265
%N A202141 a(n) = 13*n^2 - 16*n + 5.
%C A202141 Numbers of the form (r*n - r + 1)^2 + ((r+1)*n - r)^2; in this case, r=2.
%C A202141 Inverse binomial transform of this sequence: 5,-3, 26, 0, 0 (0 continued).
%H A202141 Bruno Berselli, <a href="/A202141/b202141.txt">Table of n, a(n) for n = 0..1000</a>
%H A202141 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A202141 G.f.: (5 - 13*x + 34*x^2)/(1-x)^3.
%F A202141 a(n) = A161587(n-1) + 1 with A161587(-1) = 4.
%F A202141 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. - _Wesley Ivan Hurt_, Oct 09 2017
%F A202141 E.g.f.: (5 - 3*x + 13*x^2)*exp(x). - _Elmo R. Oliveira_, Oct 20 2024
%p A202141 A202141:=n->13*n^2-16*n+5: seq(A202141(n), n=0..100); # _Wesley Ivan Hurt_, Oct 09 2017
%t A202141 Table[13 n^2 - 16 n + 5, {n, 0, 42}]
%t A202141 LinearRecurrence[{3,-3,1},{5,2,25},50] (* _Harvey P. Dale_, Aug 23 2025 *)
%o A202141 (PARI) for(n=0, 42, print1(13*n^2-16*n+5", "));
%o A202141 (Magma) [13*n^2-16*n+5: n in [0..42]];
%Y A202141 Cf. A190816 (r=1), A154355 (r=3), A161587.
%K A202141 nonn,easy,changed
%O A202141 0,1
%A A202141 _Bruno Berselli_, Dec 12 2011