OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
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
EXAMPLE
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;
...
PROG
(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
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Philippe Deléham, Dec 02 2003
EXTENSIONS
a(31) corrected and terms a(32) and beyond from Andrew Howroyd, Jun 05 2021
STATUS
approved