OFFSET
1,2
COMMENTS
The ratio a(n+1)/a(n) alternates between 5.3722813232690143299 and 1.3722813232690143299.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,9,0,-12).
FORMULA
Given the auxiliary b(0)=b(1)=1 and b(n) = b(n-1)/2 + b(n-2) *sqrt(5-(-1)^n*4) /2, a(n) =2^(n-1)*b(n).
a(n) = a(n-1)+6*a(n-2) if n is odd. a(n) = a(n-1)+2*a(n-2) if n is even. - R. J. Mathar, Jun 18 2014
MATHEMATICA
a[1] := 1; a[2]=1;
a[n_] := a[n] = a[n - 1]/2 +a[n - 2]*Sqrt[(5 + 4*(-1)^(n - 1))]//2:
Table[2^(n - 1)*a[n], {n, 1, 30}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Roger L. Bagula, Apr 29 2010
STATUS
approved