OFFSET
1,1
COMMENTS
A bisection of A001445.
a(n) written in base 2: 101, 10010, 1000100, 100001000, ..., i.e. number 1, n times 0, number 1, (n-1) times 0 (see A164367). [Jaroslav Krizek, Aug 14 2009]
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (6,-8).
FORMULA
a(n) = A001445(2n+1).
a(n) = 6*a(n-1) - 8*a(n-2).
G.f.: x*(5-12*x)/((1-4*x)*(1-2*x)).
E.g.f.: (-3 + exp(2*x) + 2*exp(4*x))/2. - Ilya Gutkovskiy, Jun 21 2016
MATHEMATICA
Table[2^(2 n) + 2^(n - 1), {n, 24}] (* or *)
Rest@ CoefficientList[Series[-x (-5 + 12 x)/((4 x - 1) (2 x - 1)), {x, 0, 24}], x] (* Michael De Vlieger, Jun 21 2016 *)
LinearRecurrence[{6, -8}, {5, 18}, 30] (* Harvey P. Dale, Jan 07 2023 *)
PROG
(PARI) x='x+O('x^50); Vec(x*(5-12*x)/((1-4*x)*(1-2*x))) \\ G. C. Greubel, Sep 08 2017
(PARI) a(n) = 2^(2*n) + 2^(n-1); \\ Michel Marcus, Sep 09 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jaroslav Krizek, Aug 08 2009
EXTENSIONS
Edited and extended by R. J. Mathar, Aug 11 2009
STATUS
approved