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

1,2

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

Links

Table of n, a(n) for n=1..54.

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

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

Example

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.

Prog

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

Crossrefs

Cf. A000982, A007590, A131479.

Sequence in context: A337120 A100057 A007590 * A256885 A293495 A330130

Adjacent sequences: A080473 A080474 A080475 * A080477 A080478 A080479

Keyword

nonn,easy

Author

Amarnath Murthy, Mar 11 2003

Extensions

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

Status

approved