OFFSET
1,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..500
Index entries for linear recurrences with constant coefficients, signature (2,11).
FORMULA
From G. C. Greubel, Mar 04 2021: (Start)
a(n) = 2*a(n-1) + 11*a(n-2), for n>4, with a(1)=2, a(2)=22, a(3)=242, a(4)=2662.
G.f.: 2*x*(1 + 11*x + (11*x)^2*(1+9*x)/(1-2*x-11*x^2)).
G.f.: 2*x*(1 +9*x +88*x^2 +968*x^3)/(1-2*x-11*x^2).
a(n) = 2*a(n-1) + prime(j)*a(n-2), for n > 4, with a(1) = 2, a(2) = 2*prime(j), a(3) = 2*prime(j)^2, a(4) = 2*prime(j)^3 for j = 5.
a(n) = 2*(prime(j)-3)*[n=1] -2*prime(j)*(prime(j)-3)*[n=2] +2*prime(j)^2*(i*sqrt(prime(j)))^(n-3)*(ChebyshevU(n-3, -i/Sqrt(prime(j))) -((prime(j) -2)*i/sqrt(prime(j)))*ChebyshevU(n-4, -i/sqrt(prime(j)))) for j = 5. (End)
MAPLE
m:= 40;
S:= series( x*(2 +18*x +176*x^2 +1936*x^3)/(1-2*x-11*x^2), x, m+1);
seq(coeff(S, x, j), j = 1..m); # G. C. Greubel, Mar 04 2021
MATHEMATICA
LinearRecurrence[{2, 11}, {2, 22, 242, 2662}, 40] (* G. C. Greubel, Mar 04 2021 *)
PROG
(Sage)
def A151617_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( 2*x*(1 +9*x +88*x^2 +968*x^3)/(1-2*x-11*x^2) ).list()
a=A151617_list(41); a[1:] # G. C. Greubel, Mar 04 2021
(Magma)
R<x>:=PowerSeriesRing(Integers(), 41);
Coefficients(R!( 2*x*(1 +9*x +88*x^2 +968*x^3)/(1-2*x-11*x^2) )); // G. C. Greubel, Mar 04 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, May 29 2009
EXTENSIONS
Terms a(11) onward added by G. C. Greubel, Mar 04 2021
STATUS
approved