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%I #38 Feb 18 2023 19:01:32
%S 1,2,4,8,12,18,24,32,40,50,60,72,84,98,112,128,144,162,180,200,220,
%T 242,264,288,312,338,364,392,420,450,480,512,544,578,612,648,684,722,
%U 760,800,840,882,924,968,1012,1058,1104,1152,1200,1250,1300,1352,1404,1458
%N Floor( geometric mean of next n numbers ).
%C Essentially the same as A007590: a(n) = A007590(n) for n>=2.
%C Also, floor( harmonic mean of next n numbers ).
%C Also, floor(sqrt(A131479(n)+1)). - _Richard R. Forberg_, Aug 04 2013
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).
%F a(n+3) = 2*a(n+2) - a(n+1) if n even, a(n+3) = 2*a(n+2) - a(n+1) + 2 if n odd, with a(1) = 1, a(2) = 2, a(3) = 4. - _Yosu Yurramendi_, Sep 12 2008
%F From _Colin Barker_, Aug 08 2013: (Start)
%F a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n > 5.
%F G.f.: x*(x^4 - 2*x^3 - 1)/((x - 1)^3*(x + 1)). (End)
%F E.g.f.: (2*x + x*(x + 1)*cosh(x) + (x^2 + x - 1)*sinh(x))/2. - _Stefano Spezia_, Feb 18 2023
%e a(4) = floor( (7*8*9*10)^(1/4) ) = 8.
%e a(4) = floor( 1/( (1/7 + 1/8 + 1/9 + 1/10 )*(1/4)) ) = 8.
%o (PARI) a(n)=if(n<2,n>0,n^2\2);
%Y Cf. A000982, A007590, A131479.
%K nonn,easy
%O 1,2
%A _Amarnath Murthy_, Mar 11 2003
%E More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003
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