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%I #21 Oct 13 2020 19:06:39
%S 5,25,61,113,181,265,365,481,613,761,925,1105,1301,1513,1741,1985,
%T 2245,2521,2813,3121,3445,3785,4141,4513,4901,5305,5725,6161,6613,
%U 7081,7565,8065,8581,9113,9661,10225,10805,11401,12013,12641,13285,13945,14621,15313
%N (2*n-1)^2 + (2*n)^2.
%D Marilyn vos Savant and Leonore Fleischer, Brain Building in Just 12 Weeks, Bantam Books, New York, NY, 1991, pp. 104-105, 119.
%H Harry J. Smith, <a href="/A060820/b060820.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F 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 a(1)=5 because 1^2+2^2=5. a(2)=25 because 3^2+4^2=25.
%t Table[(2*n - 1)^2 + (2*n)^2, {n, 300}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 16 2012 *)
%t LinearRecurrence[{3,-3,1},{5,25,61},60] (* _Harvey P. Dale_, Oct 13 2020 *)
%o (PARI) for (n=1, 1000, write("b060820.txt", n, " ", (2*n - 1)^2 + (2*n)^2); ) \\ _Harry J. Smith_, Jul 12 2009
%K easy,nonn
%O 1,1
%A _Jason Earls_, May 05 2001
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