A171648 a(1) = 1, a(n) = 2*a(n-1) if n is even; a(n) = a(n-1)*Fibonacci((n+1)/2)/Fibonacci((n-1)/2) if n is odd.

1, 2, 2, 4, 8, 16, 24, 48, 80, 160, 256, 512, 832, 1664, 2688, 5376, 8704, 17408, 28160, 56320, 91136, 182272, 294912, 589824, 954368, 1908736, 3088384, 6176768, 9994240, 19988480, 32342016, 64684032, 104660992, 209321984, 338690048, 677380096, 1096024064

Offset: 1

Author

Gary W. Adamson, Dec 13 2009

Keywords

• nonn
• easy

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

Examples

			a(8) = 48 = 2*a(7) = 2*24. a(9) = 80 = (5/3)*48 since Fibonacci(5) = 5 and Fibonacci(4) = 3.
		

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).

Crossrefs

Cf. A063727 (bisection), A103435 (bisection).

Programs

PARI

Vec(x*(1+2*x)/(1-2*x^2-4*x^4) + O(x^50)) \\ Colin Barker, Aug 02 2016

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)

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