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%I #12 Jan 11 2018 15:06:25
%S 1,35,90,3150,8100,283500,729000,25515000,65610000,2296350000,
%T 5904900000,206671500000,531441000000,18600435000000,47829690000000,
%U 1674039150000000,4304672100000000,150663523500000000,387420489000000000,13559717115000000000,34867844010000000000
%N Expansion of (1+35*x)/(1-90*x^2).
%C a(1) = 1, a(2) = 35, for n >= 3; a(n) = the smallest number h > a(n-1) such that [[a(n-2) + a(n-1)] * [a(n-2) + h] * [a(n-1) + h]] / [a(n-2) * a(n-1) * h] is integer (= 130). (conjectured)
%C 10^(floor((n - 1)/2)) | a(n), for n>=1. - _G. C. Greubel_, Jan 11 2018
%H G. C. Greubel, <a href="/A182755/b182755.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,90).
%F a(2n) = 35* a(2n-1), a(2n+1) = 18/7 * a(2n).
%F a(2n) = 35*90^(n-1), a(2n+1) = 90^n.
%e For n = 4; a(2) = 35, a(3) = 90, a(4) = 3150 before [(35+90)*(35+3150)*(90+3150)] / (35*90*3150) = 130.
%t LinearRecurrence[{0,90}, {1,35}, 50] (* or *) CoefficientList[Series[(1 + 35*x)/(1-90*x^2), {x,0,50}], x] (* _G. C. Greubel_, Jan 11 2018 *)
%o (PARI) Vec((1+35*x)/(1-90*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 25 2012
%o I:=[1,35]; [n le 2 select I[n] else 90*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 11 2018
%Y Cf. A182751, A182752, A182753, A182754, A182756, A182757, A038754.
%K nonn,easy
%O 1,2
%A _Jaroslav Krizek_, Nov 27 2010
%E Terms a(12) onward added by _G. C. Greubel_, Jan 11 2018
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