OFFSET
0,2
COMMENTS
a(n)/a(n-1) tends to phi. (Cf. A062114).
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,2,-1,-1).
FORMULA
a(n) = -3*(1+(-1)^n)/2 +4*A000045(n+1). - R. J. Mathar, Aug 13 2012
G.f.: ( 1+3*x-x^2 ) / ( (x-1)*(1+x)*(x^2+x-1) ). - R. J. Mathar, Aug 13 2012
From Colin Barker, Jul 12 2017: (Start)
a(n) = (2^(1-n)*((1+sqrt(5))^(n+1) - (1-sqrt(5))^(n+1))) / sqrt(5) - 3 for n even.
a(n) = (2^(1-n)*((1+sqrt(5))^(n+1) - (1-sqrt(5))^(n+1))) / sqrt(5) for n odd.
a(n) = a(n-1) + 2*a(n-2) - a(n-3) - a(n-4) for n>3.
(End)
EXAMPLE
PROG
(PARI) Vec((1 + 3*x - x^2) / ((1 - x)*(1 + x)*(1 - x - x^2)) + O(x^50)) \\ Colin Barker, Jul 12 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Jun 28 2007
EXTENSIONS
More terms from Colin Barker, Jul 12 2017
STATUS
approved