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%I #22 May 04 2018 11:34:40
%S 0,9,60,357,2088,12177,70980,413709,2411280,14053977,81912588,
%T 477421557,2782616760,16218279009,94527057300,550944064797,
%U 3211137331488,18715879924137,109084142213340,635788973355909,3705649697922120,21598109214176817,125883005587138788
%N Values of k such that k^2 + (k+3)^2 is a square.
%C A075841 gives the corresponding values of sqrt(n^2 + (n+3)^2).
%H Vincenzo Librandi, <a href="/A241976/b241976.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,1).
%F G.f.: 3*x^2*(x-3) / ((x-1)*(x^2-6*x+1)).
%F a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3).
%F a(n) = 3*A001652(n-1).
%F a(n) = -3*(2 + (3-2*sqrt(2))^n*(1+sqrt(2)) - (-1+sqrt(2))*(3+2*sqrt(2))^n) / 4. - _Colin Barker_, Apr 13 2017
%e 9 is in the sequence because 9^2 + 12^2 = 225 = 15^2.
%t CoefficientList[Series[3 x (x - 3)/((x - 1) (x^2 - 6 x + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 11 2014 *)
%o (PARI) concat(0, Vec(3*x^2*(x-3)/((x-1)*(x^2-6*x+1)) + O(x^100)))
%Y Cf. A001652, A065113, A075841.
%K nonn,easy
%O 1,2
%A _Colin Barker_, Aug 10 2014
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