A131479 -id:A131479 - cp's OEIS frontend

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

Amarnath Murthy, Mar 11 2003

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

			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.

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

Cf. A000982, A007590, A131479.

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

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

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

A131478 a(n) = ceiling(n^4/4).

Original entry on oeis.org

0, 1, 4, 21, 64, 157, 324, 601, 1024, 1641, 2500, 3661, 5184, 7141, 9604, 12657, 16384, 20881, 26244, 32581, 40000, 48621, 58564, 69961, 82944, 97657, 114244, 132861, 153664, 176821, 202500, 230881, 262144, 296481, 334084, 375157, 419904, 468541, 521284

Offset: 0

Mohammad K. Azarian, Jul 27 2007

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-5,0,5,-4,1).

Cf. A000982, A004526, A007590, A008619, A036487, A058919.

Cf. A131479.

[Ceiling(n^4/4) : n in [0..50]]; // Vincenzo Librandi, Oct 01 2011

Ceiling[Range[0,40]^4/4] (* Harvey P. Dale, May 17 2019 *)
CoefficientList[Series[(x(x^3 + 6x^2 + 7x + 1)Cosh[x]+ (x^4 + 6x^3 + 7x^2 + x + 3)Sinh[x])/4,{x,0,35}],x]Table[n!,{n,0,35}] (* Stefano Spezia, Feb 19 2023 *)

vector(50, n, n--;ceil(n^4/4)) \\ Michel Marcus, Jun 16 2015

def A131478(n): return n**4+3>>2 # Chai Wah Wu, Jan 30 2023

From R. J. Mathar, Dec 19 2008: (Start)
G.f.: x*(1 + 10*x^2 + x^4)/((1 - x)^5*(1 + x)).
a(n) + a(n+1) = A058919(n+1). (End)
a(n) = floor(n^4/4 + 3/4). - Bruno Berselli, Dec 21 2017
E.g.f.: (x*(x^3 + 6*x^2 + 7*x + 1)*cosh(x) + (x^4 + 6*x^3 + 7*x^2 + x + 3)*sinh(x))/4. - Stefano Spezia, Feb 18 2023

cp's OEIS Frontend

A080476 Floor( geometric mean of next n numbers ).

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