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%I #18 Jun 17 2017 00:01:53
%S 13,39,79,133,201,283,379,489,613,751,903,1069,1249,1443,1651,1873,
%T 2109,2359,2623,2901,3193,3499,3819,4153,4501,4863,5239,5629,6033,
%U 6451,6883,7329,7789,8263,8751,9253,9769,10299,10843,11401,11973,12559,13159,13773
%N 1+5*n+7*n^2.
%C Consider the quadratic cyclotomic polynomial f(x) = x^2+x+1 and the quotients defined by f(x + n*f(x))/f(x). a(n) is the quotient at x=2.
%C See A168240 for x=3 or A168244 for x= 1+sqrt(-5).
%H Harvey P. Dale, <a href="/A168235/b168235.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(1)=13, a(2)=39, a(3)=79, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). - _Harvey P. Dale_, Feb 07 2015
%F From _G. C. Greubel_, Apr 09 2016: (Start)
%F G.f.: (1 + 10*x + 3*x^2)/(1-x)^3.
%F E.g.f.: (1 + 12*x + 7*x^2)*exp(x). (End)
%e When x = 2, f(x) = 7. Hence at n=1, f( x + f(x))/f(x) = 13 = a(1).
%t Table[1+5n+7n^2,{n,60}] (* or *) LinearRecurrence[{3,-3,1},{13,39,79},60] (* _Harvey P. Dale_, Feb 07 2015 *)
%o (PARI) a(n)=1+5*n+7*n^2 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A165806, A165808, A165809.
%K nonn,easy
%O 1,1
%A _A.K. Devaraj_, Nov 21 2009
%E Edited, definition simplified, sequence extended beyond a(8) by _R. J. Mathar_, Nov 23 2009
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