0,2

Harmonious sequence, build on the number 8.1231056... a(n+1)/a(n) converges to 4+sqrt(17). a(0)/a(1)=1/4; a(1)/a(2)=4/33; a(2)/a(3)=33/268; a(3)/a(4)=268/2177;...etc. Lim a(n)/a(n+1)as n approaches infinity=0.123105625...=1/(4+sqrt(17))=sqrt(17)-4.

Tanya Khovanova, Recursive Sequences

Index entries for sequences related to Chebyshev polynomials.

a(n) = 8a(n-1) + a(n-2), starting with a(0) = 1 and a(1) = 4. a(n) = ([(8+sqrt(68))/2]^n + [(8-sqrt(68))/2]^n)/2. a(n) = A086594(n)/2

E.g.f. : exp(4x)cosh(sqrt(17)x); a(n)=((4+sqrt(17))^n+(4-sqrt(17))^n)/2; a(n)=sum{k=0..floor(n/2), C(n, 2k)17^k4^(n-2k)}. a(n)=T(n, 4i)(-i)^n with T(n, x) Chebyshev's polynomials of the first kind (see A053120), and i^2=-1. - Paul Barry (pbarry(AT)wit.ie), Nov 15 2003

a(4) = 2177 = 8a(3) + a(2) = 8*268 + 33 = ([(8+sqrt(68))/2]^4 + [(8-sqrt(68))/2]^4)/2 = (4353.9997703+ 0.0002297)/2=2177.

Cf. A002018, A002190, A013192, A028576, A041027, A058153, A058155, A072754, A075132.

Cf. A041024.

Sequence in context: A097705 A131509 A081007 this_sequence A041024 A123780 A054371

Adjacent sequences: A088314 A088315 A088316 this_sequence A088318 A088319 A088320

easy,nonn

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Nov 06 2003