A080476 Floor( geometric mean of next n numbers ).

1, 2, 4, 8, 12, 18, 24, 32, 40, 50, 60, 72, 84, 98, 112, 128, 144, 162, 180, 200, 220, 242, 264, 288, 312, 338, 364, 392, 420, 450, 480, 512, 544, 578, 612, 648, 684, 722, 760, 800, 840, 882, 924, 968, 1012, 1058, 1104, 1152, 1200, 1250, 1300, 1352, 1404, 1458

Offset: 1

Author

Amarnath Murthy, Mar 11 2003

Keywords

• nonn
• easy

Comments

Essentially the same as A007590: a(n) = A007590(n) for n>=2.

Also, floor( harmonic mean of next n numbers ).

Also, floor(sqrt(A131479(n)+1)). - Richard R. Forberg, Aug 04 2013

Examples

			a(4) = floor( (7*8*9*10)^(1/4) ) = 8.
a(4) = floor( 1/( (1/7 + 1/8 + 1/9 + 1/10 )*(1/4)) ) = 8.
		

Links

• Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Crossrefs

Cf. A000982, A007590, A131479.

Programs

PARI

a(n)=if(n<2,n>0,n^2\2);

Formula

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

From Colin Barker, Aug 08 2013: (Start)

a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n > 5.

G.f.: x*(x^4 - 2*x^3 - 1)/((x - 1)^3*(x + 1)). (End)

E.g.f.: (2*x + x*(x + 1)*cosh(x) + (x^2 + x - 1)*sinh(x))/2. - Stefano Spezia, Feb 18 2023

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003