A117465 Denominator of -16/((n+2)*n*(n-2)*(n-4)).

9, 0, 15, 0, 105, 24, 945, 120, 3465, 360, 9009, 840, 19305, 1680, 36465, 3024, 62985, 5040, 101745, 7920, 156009, 11880, 229425, 17160, 326025, 24024, 450225, 32760, 606825, 43680, 801009, 57120, 1038345, 73440, 1324785, 93024, 1666665, 116280

Offset: 1

Author

Steven J. Forsberg, Apr 25 2006

Keywords

• frac
• nonn
• easy

Comments

I came up with the equation to help analyze the path to stable orbits of the logistic function

f(n+1) = k*n(1-n) for f(n) with n => 9, then f(n)*A072346(n-5) = A072346(n+3).

a(n) is the denominator of f(n). The numerator of f(n) is -1 if n is even, else -16.

Examples

			f(5) = -16/(7*5*3*1) = -16/105, denominator a(5) = 105.
f(6) = -16/(8*6*4*2) = -1/24, denominator a(6) = 24.
		

Links

• Colin Barker, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,5,0,-10,0,10,0,-5,0,1).

Crossrefs

Cf. A052762, A072346.

Programs

Maple

f(n) := n -> (1/((n/4)+(n^2/4)-(n^3/16)-1))/n;

Mathematica

Join[{9,0,15,0},Denominator[Table[-(16/(n (n^3-4 n^2-4 n+16))), {n,5,40}]]]    (* Harvey P. Dale, Nov 06 2011 *)

PARI

Vec(3*x*(10*x^12-50*x^10+105*x^8-160*x^6-8*x^5-40*x^4+10*x^2-3)/((x-1)^5*(x+1)^5) + O(x^100)) \\ Colin Barker, Nov 11 2014

Formula

a(n) = denominator of the reduced -16/(n*(n-2)*(n+2)*(n-4)).

a(2n) = A052762(n+1).

a(n) = 5*a(n-2) -10*a(n-4) +10*a(n-6) -5*a(n-8) +a(n-10) for n>15. - R. J. Mathar, Mar 27 2010

a(n) = -(-17+15*(-1)^n)*(n*(16-4*n-4*n^2+n^3))/32 for n>3. - Colin Barker, Nov 11 2014

G.f.: 3*x*(10*x^12-50*x^10+105*x^8-160*x^6-8*x^5-40*x^4+10*x^2-3) / ((x-1)^5*(x+1)^5). - Colin Barker, Nov 11 2014

Extensions

Clearer definition from R. J. Mathar, Mar 27 2010