cp's OEIS Frontend

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.

A060820 a(n) = (2*n-1)^2 + (2*n)^2.

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%I A060820 #26 Jul 13 2025 16:15:10
%S A060820 5,25,61,113,181,265,365,481,613,761,925,1105,1301,1513,1741,1985,
%T A060820 2245,2521,2813,3121,3445,3785,4141,4513,4901,5305,5725,6161,6613,
%U A060820 7081,7565,8065,8581,9113,9661,10225,10805,11401,12013,12641,13285,13945,14621,15313
%N A060820 a(n) = (2*n-1)^2 + (2*n)^2.
%D A060820 Marilyn vos Savant and Leonore Fleischer, Brain Building in Just 12 Weeks, Bantam Books, New York, NY, 1991, pp. 104-105, 119.
%H A060820 Harry J. Smith, <a href="/A060820/b060820.txt">Table of n, a(n) for n = 1..1000</a>
%H A060820 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A060820 a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). G.f.: x*(5+10*x+x^2)/(1-x)^3. - _Colin Barker_, Apr 22 2012
%e A060820 a(1)=5 because 1^2+2^2=5. a(2)=25 because 3^2+4^2=25.
%t A060820 Table[(2*n - 1)^2 + (2*n)^2, {n, 300}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 16 2012 *)
%t A060820 LinearRecurrence[{3,-3,1},{5,25,61},60] (* _Harvey P. Dale_, Oct 13 2020 *)
%o A060820 (PARI) a(n) = (2*n - 1)^2 + (2*n)^2 \\ _Harry J. Smith_, Jul 12 2009
%Y A060820 Essentially identical to A080856, which is the main entry for this sequence. - _N. J. A. Sloane_, Jul 13 2025
%K A060820 easy,nonn
%O A060820 1,1
%A A060820 _Jason Earls_, May 05 2001