OFFSET
0,3
COMMENTS
Starting with n=2, binary numbers of the form (n-1)0(n) where n is the index and the number of 1's. It can also be formed by appending a 1 to the right of each term of A129868.
1/a(n) = Sum_{m>0} A000045(m)*2^(-n(m+1)) for n > 0. E.g., 1/a(4) = 0.0000 0001 0001 0010 0011 0101 1000 ... in binary. - Lee A. Newberg, Apr 12 2018
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (7,-14,8).
FORMULA
G.f.: ( 1-8*x+10*x^2 ) / ( (-1+x)*(2*x-1)*(4*x-1) ). - R. J. Mathar, Oct 21 2014
MATHEMATICA
Table[4^n - 2^n - 1, {n, 0, 25}] (* Vincenzo Librandi, Apr 13 2018 *)
PROG
(PARI) vector(99, n, 4^n-2^n-1)
(Magma) [4^n-2^n-1: n in [0..30]]; // Vincenzo Librandi, Apr 13 2018
CROSSREFS
KEYWORD
sign,easy
AUTHOR
M. F. Hasler, Feb 10 2009
STATUS
approved