OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,3,-2,-1,-1,-3,2,1,1,1).
FORMULA
G.f.: x*(3 +3*x +2*x^2 -2*x^3 -4*x^4 -x^5 -2*x^6)/((1-x-x^2)*(1-x^2-x^4)^2). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 27 2009
From G. C. Greubel, Jan 16 2022: (Start)
a(2*n) = L(2*n+4) + F(2*n+3) - F(n+5) - (n+2)*F(n+3), n >= 1.
MATHEMATICA
a[n_]:= With[{F=Fibonacci}, If[EvenQ[n], LucasL[n+4] +F[n+3] -F[(n+10)/2] -((n+ 4)/2)*F[(n+6)/2], LucasL[n+4] +F[n+3] -F[(n+7)/2] -((n+7)/2)*F[(n+5)/2]]];
Table[a[n], {n, 40}] (* G. C. Greubel, Jan 16 2022 *)
PROG
(Magma)
R<x>:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( x*(3+3*x+2*x^2-2*x^3-4*x^4-x^5-2*x^6)/((1-x-x^2)*(1-x^2-x^4)^2) )); // G. C. Greubel, Jan 16 2022
(Sage)
def A024315_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( x*(3+3*x+2*x^2-2*x^3-4*x^4-x^5-2*x^6)/((1-x-x^2)*(1-x^2-x^4)^2) ).list()
a=A024315_list(41); a[1:] # G. C. Greubel, Jan 16 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved