OFFSET
0,3
COMMENTS
LINKS
Robert Israel, Table of n, a(n) for n = 0..1606
FORMULA
Conjecture: a(n) = 2*a(n-1)+12*a(n-2)-8*a(n-3)-16*a(n-4). G.f.: x*(4*x^2+1) / (16*x^4+8*x^3-12*x^2-2*x+1). [Colin Barker, Jan 17 2013]
Confirmation of conjecture by Robert Israel, Jan 01 2018: (Start)
The polynomials p(n,x) have g.f. G(z) = (1-x*z)/(1-2*x*z-5*z^2-x*z^2+x^2*z^2).
The reductions mod x^2-x-1 have g.f. g(z) = (1+x*z-2*z-6*z^2+4*x*z^3)/(1-2*z-12*z^2+8*z^3+16*z^4):
note that the numerator of G(z)-g(z) is divisible by x^2-x-1. (End)
EXAMPLE
MAPLE
f:= gfun:-rectoproc({a(n) = 2*a(n-1)+12*a(n-2)-8*a(n-3)-16*a(n-4), a(0)=0, a(1)=1, a(2)=2, a(3)=20}, a(n), remember):
map(f, [$0..50]); # Robert Israel, Jan 01 2018
MATHEMATICA
(See A192350.)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jun 28 2011
EXTENSIONS
Offset corrected by Robert Israel, Jan 01 2018
STATUS
approved