A175784 Numerators of k/(10+k)+1 for k = 2*n-1.

12, 16, 4, 24, 28, 32, 36, 8, 44, 48, 52, 56, 12, 64, 68, 72, 76, 16, 84, 88, 92, 96, 20, 104, 108, 112, 116, 24, 124, 128, 132, 136, 28, 144, 148, 152, 156, 32, 164, 168, 172, 176, 36, 184, 188, 192, 196, 40, 204, 208, 212, 216, 44, 224, 228

Offset: 1

Author

Steven J. Forsberg, Dec 04 2010

Keywords

• nonn

Comments

For even k the expression k/(k+10)+1 yields A060791 as denominators, A096431 as numerators. For odd k it yields A096431 as denominators, the present sequence as numerators.

Note that A096431 is denominator of (9*(n^4 - 2n^3 + 2n^2 - n) + 2)/(2*(2*n-1)), equivalently denominator of (3*n^2 - 3*n + 1)*(3*n^2 - 3*n + 2)/(2*n-1), and that A060791 is n/gcd(n,5).

Examples

			n=1: (2*1-1)/(2*1+9)+1 = 1/11+1 = 12/11, hence a(1) = 12;
n=2: (2*2-1)/(2*2+9)+1 = 3/13+1 = 16/13, hence a(2) = 16;
n=3: (2*3-1)/(2*3+9)+1 = 5/15+1 = 1/3+1 = 4/3, hence a(3) = 4;
		

Crossrefs

Cf. A096431, A060791.

Programs

Maple

A175784 := proc(n) local k ; k := 2*n-1 ; numer(k/(10+k)+1) ; end proc:
seq(A175784(n),n=1..30) ; # R. J. Mathar, Feb 05 2011

Mathematica

Numerator[Table[k/(10 + k) + 1, {k, 1, 100, 2}]]

Formula

a(n) = numerator((2*n-1)/(2*n+9) + 1).

Conjecture: a(n) = 2*a(n-5) - a(n-10) = 4*A060791(n+2) with g.f. -4*x*(-3 - 4*x - x^2 - 6*x^3 - 7*x^4 - 2*x^5 - x^6 + x^8 + 2*x^9) / ( (x-1)^2*(x^4 + x^3 + x^2 + x + 1)^2 ). [R. J. Mathar, Dec 07 2010]