0,1

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)=8/66; a(2)/a(3)=66/536; a(3)/a(4)=536/4354;...etc. Lim a(n)/a(n+1)as n approaches infinity=0.123105625...=1/(4+sqrt(17))=sqrt(17)-4.

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)

a(n)=(4+sqrt(17))^n+(4-sqrt(17))^n.

O.g.f: 2*(-1+4*x)/(-1+8*x+x^2) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 02 2007

a(4)=4354=8a(3)+a(2)=8*536+66=(4+sqrt(17))^4+(4-sqrt(17))^4=4353.9997703+

0.0002297=4354.

Cf. A003285.

Sequence in context: A009602 A011836 A100623 this_sequence A132219 A023164 A053922

Adjacent sequences: A086591 A086592 A086593 this_sequence A086595 A086596 A086597

easy,nonn

Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 11 2003