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%I #13 Sep 08 2022 08:45:55
%S 1,14,35,490,1225,17150,42875,600250,1500625,21008750,52521875,
%T 735306250,1838265625,25735718750,64339296875,900750156250,
%U 2251875390625,31526255468750,78815638671875,1103418941406250,2758547353515625,38619662949218750,96549157373046875
%N Expansion of (1 + 14*x)/(1 - 35*x^2).
%C a(1) = 1, a(2) = 14, 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 (= 54).
%C 5^(floor((n - 1)/2)) | a(n), n>=1. - _G. C. Greubel_, Jan 11 2018
%H G. C. Greubel, <a href="/A182753/b182753.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 (0,35).
%F a(2n) = 14 * a(2n-1), a(2n+1) = 5/2 * a(2n).
%F a(2n) = 14*35^(n-1), a(2n+1) = 35^n.
%e For n = 5; a(3) = 35, a(4) = 490, a(5) = 1225 before [(35+490)*(35+1225)*(490+1225)] / (35*490*1225) = 54.
%t LinearRecurrence[{0, 35}, {1, 14}, 30] (* or *) CoefficientList[Series[(1 + 14*x)/(1-35*x^2), {x,0,50}], x] (* _G. C. Greubel_, Jan 11 2018 *)
%o (PARI) Vec((1+14*x)/(1-35*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 25 2012
%o (Magma) I:=[1,14]; [n le 2 select I[n] else 35*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 11 2018
%Y Cf. A182751, A182752, A182754, A182755, A182756, A182757.
%K nonn,easy
%O 1,2
%A _Jaroslav Krizek_, Nov 27 2010
%E Terms a(15) onward added by _G. C. Greubel_, Jan 11 2018
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