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A182752 a(1) = 1, a(2) = 6, for n >= 3; a(n) = the smallest number greater than a(n-1) such that [[a(n-2) + a(n-1)] * [a(n-2) + a(n)] * [a(n-1) + a(n)]] / [a(n-2) * a(n-1) * a(n)] is an integer.

%I A182752 #17 Nov 17 2022 10:02:23
%S A182752 1,6,14,84,196,1176,2744,16464,38416,230496,537824,3226944,7529536,
%T A182752 45177216,105413504,632481024,1475789056,8854734336,20661046784
%N A182752 a(1) = 1, a(2) = 6, for n >= 3; a(n) = the smallest number greater than a(n-1) such that [[a(n-2) + a(n-1)] * [a(n-2) + a(n)] * [a(n-1) + a(n)]] / [a(n-2) * a(n-1) * a(n)] is an integer.
%H A182752 Harvey P. Dale, <a href="/A182752/b182752.txt">Table of n, a(n) for n = 1..1000</a>
%H A182752 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,14).
%F A182752 a(2n) = 6 * a(2n-1), a(2n+1) = 7/3 * a(2n).
%F A182752 G.f.: (1 + 6*x)/(1 - 14*x^2). - _Georg Fischer_, Nov 17 2022
%e A182752 a(5)=196 since (14+84)*(14+x)*(84+x)/(14*84*x) is an integer for x=196, but not an integer for any x satisfying 85 <= x <= 195.
%t A182752 nxt[{n_,a_}]:={n+1,If[OddQ[n],6*a,7/3 a]}; NestList[nxt,{1,1},20][[All,2]] (* _Harvey P. Dale_, Aug 14 2020 *)
%Y A182752 Cf. A182751, A182753, A182754, A182755, A182756,  A182757.
%K A182752 nonn,easy
%O A182752 1,2
%A A182752 _Jaroslav Krizek_, Nov 27 2010