OFFSET
1,1
LINKS
FORMULA
G.f.: 2*x*(1+4*x+5*x^2)/(1-4*x^2). - Mark Thomas
From Ilya Gutkovskiy, Jul 22 2016: (Start)
E.g.f.: (-8 - 10*x + 9*sinh(2*x) + 8*cosh(2*x))/4.
a(n) = 2^(n-3)*(17 - (-1)^n), for n>1. (End)
EXAMPLE
32 = 2^5 is in the sequence (since the exponent 5 is odd), and 72 = 9*2^3 is also in the sequence. - Michael B. Porter, Jul 22 2016
MATHEMATICA
nn = 10^12; Union@ Flatten@ {#, TakeWhile[9 #, # <= nn &]} &[2^Range[1, Floor[Log2[nn]], 2]] (* or *)
Rest@ CoefficientList[Series[2 x (1 + 4 x + 5 x^2)/(1 - 4 x^2), {x, 0, 37}], x] (* Michael De Vlieger, Jul 22 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 19 2011, following a suggestion by Mark Thomas
STATUS
approved
