OFFSET
1,1
LINKS
R. H. Hardin, Table of n, a(n) for n=1..100
Index entries for linear recurrences with constant coefficients, signature (1,1).
FORMULA
a(n) = a(n-1) + a(n-2) for n>=5.
[The Transfer Matrix Method provides this recurrence. - R. J. Mathar, Aug 02 2017]
From Colin Barker, Feb 20 2018: (Start)
G.f.: x*(2 - x)*(1 + x)^2 / (1 - x - x^2).
a(n) = (2^(-1-n)*((1-sqrt(5))^n*(-5+sqrt(5)) + (1+sqrt(5))^n*(5+sqrt(5)))) / sqrt(5) for n>2.
(End)
EXAMPLE
All solutions for n=4:
...0.1...0.1...1.1...1.1...1.0...1.1...1.0...1.1...1.0...1.0...0.1
...0.1...0.1...0.1...0.1...1.0...1.0...1.0...1.0...1.1...1.1...1.1
...0.1...0.1...0.1...0.1...1.1...1.1...1.0...1.0...0.1...0.1...1.0
...0.1...1.1...0.1...1.1...0.1...0.1...1.1...1.1...0.1...1.1...1.1
PROG
(PARI) Vec(x*(2 - x)*(1 + x)^2 / (1 - x - x^2) + O(x^60)) \\ Colin Barker, Feb 20 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. H. Hardin, Aug 03 2009
STATUS
approved