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%I #27 Sep 09 2022 11:07:57
%S 43,6,131,418,867,1478,2251,3186,4283,5542,6963,8546,10291,12198,
%T 14267,16498,18891,21446,24163,27042,30083,33286,36651,40178,43867,
%U 47718,51731,55906,60243,64742,69403,74226,79211,84358,89667,95138,100771
%N a(n) = 81n^2 - 118n + 43.
%C The identity (6561*n^2-9558*n+3482)^2-(81*n^2-118*n+43)*(729*n-531)^2=1 can be written as A156773(n)^2-a(n)*A156771(n)^2=1 for n>0.
%C For n >= 1, the continued fraction expansion of sqrt(a(n)) is [9n-7; {2, 4, 9n-7, 4, 2, 18n-14}]. For n=1, this collapses to [2; {2, 4}]. - _Magus K. Chu_, Sep 09 2022
%H Vincenzo Librandi, <a href="/A156677/b156677.txt">Table of n, a(n) for n = 0..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).
%F G.f.: (-43+123*x-242*x^2)/(x-1)^3.
%F For n>1: a(n) = A171198(n-2) - A017305(n-2). [From _Reinhard Zumkeller_, Jul 13 2010]
%t LinearRecurrence[{3,-3,1},{43,6,131},40]
%o (Magma) I:=[43, 6, 131]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
%o (PARI) a(n)=81*n^2-118*n+43 \\ _Charles R Greathouse IV_, Dec 23 2011
%Y Cf. A156771, A156773.
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Feb 15 2009
%E Edited by _Charles R Greathouse IV_, Jul 25 2010
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