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%I #27 Sep 20 2023 17:13:31
%S 1,6,9,24,36,96,144,384,576,1536,2304,6144,9216,24576,36864,98304,
%T 147456,393216,589824,1572864,2359296,6291456,9437184,25165824,
%U 37748736,100663296,150994944,402653184,603979776,1610612736,2415919104
%N Expansion of g.f. (1 + 6*x + 5*x^2)/((1-2*x)*(1+2*x)).
%C Binomial transform is A085287.
%H Vincenzo Librandi, <a href="/A084431/b084431.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,4).
%F a(n) = (-10*0^n - 3*(-2)^n + 21*2^n)/8.
%F a(n) = 4*a(n-2), n > 1. - _Harvey P. Dale_, Nov 05 2011
%F E.g.f.: (9*cosh(2*x) + 12*sinh(2*x) - 5)/4. - _Stefano Spezia_, Sep 20 2023
%t CoefficientList[Series[(1+6x+5x^2)/((1-2x)(1+2x)),{x,0,30}],x] (* or *) Join[{1},Flatten[NestList[4#&,{6,9},15]]] (* _Harvey P. Dale_, Nov 05 2011 *)
%o (Magma) [(-10*0^n-3*(-2)^n+21*2^n)/8: n in [0..30]]; // _Vincenzo Librandi_, Nov 16 2011
%Y Bisections are A002023 and A002063.
%Y Cf. A085287.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Jun 26 2003
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