OFFSET
0,2
COMMENTS
The first differences appear to be some kind of ruler sequence separated by 2's.
indeed, the first differences look like n -> f(A001511(n)) with f = (2, 3, 8, 33, 138, 563, 2268, 9093, 36398, 145623, 582528, 2330153, 9320658, etc.). See A340495. - Rémy Sigrist, Jan 10 2021
LINKS
Rémy Sigrist, Table of n, a(n) for n = 0..8191
Rémy Sigrist, PARI program for A340494
FORMULA
The generating function appears to be
1/(1-x ) + 2*x/(1-x)^2 + (1/(1-x))*Sum_{t>=1} x^(2^t)*(g(t+1)-g(t))/(1-x^(2^t)),
where g = {g(t): t >= 1} = 2,3,8,33,138,... has g.f. x*(2*x-1)*(2*x^2+5*x-2)/((1-x)^2*(1-4*x)). - Rémy Sigrist and N. J. A. Sloane, Jan 10 2021
PROG
(PARI) See Links section.
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 10 2021
EXTENSIONS
More terms from Rémy Sigrist, Jan 10 2021
STATUS
approved