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%I #23 Aug 19 2022 05:57:26
%S 1,5,9,5,1,45,169,245,81,125,1849,5445,6241,845,8649,70805,167281,
%T 146205,1369,465125,2556801,4890605,3052009,266805,21613201,87654845,
%U 135419769,53235845,48427681,909226125,2862999049,3521061845,659000241,3754622045
%N Expansion of x*(1+2*x)/((1-2*x)*(1-x+4*x^2)).
%C Numbers in the sequence are alternatively products of squares or five times a product of squares.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-6,8).
%F G.f.: x*(1+2*x)/((1-2*x)*(1-x+4*x^2)).
%F a(n) = 3*a(n-1) - 6*a(n-2) + 8*a(n-3) for n > 3.
%F a(n) = A112259(n)/(A112260(n))^2.
%F 3*a(n) = 2^(n+1) - A272931(n). - _R. J. Mathar_, Aug 19 2022
%e a(11) = 43^2, a(12) = 5*3^2*11^2.
%t LinearRecurrence[{3,-6,8},{1,5,9},34] (* _Stefano Spezia_, Sep 19 2020 *)
%Y Cf. A112259, A112260.
%K nonn,easy
%O 1,2
%A _Philippe Deléham_, Sep 18 2020
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