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%I #28 Sep 09 2022 11:07:22
%S 21,112,275,510,817,1196,1647,2170,2765,3432,4171,4982,5865,6820,7847,
%T 8946,10117,11360,12675,14062,15521,17052,18655,20330,22077,23896,
%U 25787,27750,29785,31892,34071,36322,38645,41040,43507,46046,48657,51340
%N a(n) = 36*n^2 - 17*n + 2.
%C The identity (10368*n^2-4896*n+577)^2-(36*n^2-17*n+2)* (1728*n-408)^2=1 can be written as A157267(n)^2-a(n)* A157266(n)^2=1 (see also the second comment in A157267). - _Vincenzo Librandi_, Jan 27 2012
%C The continued fraction expansion of sqrt(a(n)) is [6n-2; {1, 1, 2, 1, 1, 12n-4}]. - _Magus K. Chu_, Sep 09 2022
%H Vincenzo Librandi, <a href="/A157265/b157265.txt">Table of n, a(n) for n = 1..10000</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). - _Vincenzo Librandi_, Jan 27 2012
%F G.f.: x*(21 + 49*x + 2*x^2)/(1-x)^3. - _Vincenzo Librandi_, Jan 27 2012
%F E.g.f.: (36*x^2 + 19*x + 2)*exp(x) - 2. - _G. C. Greubel_, Feb 04 2018
%t LinearRecurrence[{3,-3,1},{21,112,275},40] (* _Vincenzo Librandi_, Jan 27 2012 *)
%o (PARI) a(n)=36*n^2-17*n+2 \\ _Charles R Greathouse IV_, Jan 11 2012
%o (Magma) I:=[21, 112, 275]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Jan 27 2012
%Y Cf. A157266, A157267.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Feb 26 2009
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