A089067 a(n) = 2*a(n-1) + (-1)^n*a(floor(n/2)); a(1)=1.

1, 3, 5, 13, 23, 51, 97, 207, 401, 825, 1627, 3305, 6559, 13215, 26333, 52873, 105539, 211479, 422557, 845939, 1691053, 3383733, 6765839, 13534983, 27066661, 54139881, 108273203, 216559621, 433106027, 866238387, 1732450441, 3464953755, 6929854637, 13859814813

Offset: 1

Author

Philippe Deléham, Dec 02 2003

Keywords

• easy
• nonn

Examples

			a(2) = 2*1  + 1 =  3;
a(3) = 2*3  - 1 =  5;
a(4) = 2*5  + 3 = 13;
a(5) = 2*13 - 3 = 23;
a(6) = 2*23 + 5 = 51;
a(7) = 2*51 - 5 = 97;
...
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A011782.

Programs

PARI

seq(n)={my(a=vector(n)); a[1]=1; for(n=2, n, a[n] = 2*a[n-1] + (-1)^n*a[floor(n/2)]); a} \\ Andrew Howroyd, Jun 05 2021

Formula

Lim_{n->infinity} a(n)/2^n = 0.8067474....

G.f. A(x) satisfies (1 + A(x))/(1 + A(x^2)) = (1-x)/(1-2*x). - Gary W. Adamson, Feb 18 2010, edited by Andrew Howroyd, Jun 05 2021

Extensions

a(31) corrected and terms a(32) and beyond from Andrew Howroyd, Jun 05 2021