OFFSET
1,2
COMMENTS
a(n)/a(n-1) apparently tends to phi = A001622 if n=odd; e.g. a(21)/a(20) = 91136/56320 = 1.61818...
a(n)/a(n-2) apparently tends to 1+sqrt(5) = 3.236...= A134945; where a(21)/a(19) = 91136/28160 = 3.23636...
a(1)=1, a(2)=2, a(3)=2, for n>3 a(n)=2*a(n-1) if n is even and a(n)=2*(a(n-1)-a(n-2)+a(n-3)) if n is odd. - Vincenzo Librandi, Dec 06 2010
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,4).
FORMULA
a(1) = 1, a(n) = 2*a(n-1) if n is even; a(n) = a(n-1)*A000045((n+1)/2)/A000045((n-1)/2) if n is odd.
From Colin Barker, Aug 02 2016: (Start)
a(n) = 2*a(n-2) + 4*a(n-4) for n>4.
G.f.: x*(1+2*x) / (1-2*x^2-4*x^4).
(End)
EXAMPLE
a(8) = 48 = 2*a(7) = 2*24. a(9) = 80 = (5/3)*48 since Fibonacci(5) = 5 and Fibonacci(4) = 3.
PROG
(PARI) Vec(x*(1+2*x)/(1-2*x^2-4*x^4) + O(x^50)) \\ Colin Barker, Aug 02 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Dec 13 2009
EXTENSIONS
Defined "F", removed abundant parentheses, added punctuation to examples, added a factor to the definition, corrected a(13) and added more terms - R. J. Mathar, Dec 15 2009
STATUS
approved