login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A156570 a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=17, a(2)=65. 3
17, 65, 373, 2173, 12665, 73817, 430237, 2507605, 14615393, 85184753, 496493125, 2893773997, 16866150857, 98303131145, 572952636013, 3339412684933, 19463523473585, 113441728156577, 661186845465877, 3853679344638685 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

lim_{n -> infinity} a(n)/a(n-1) = 3+2*sqrt(2).

LINKS

Table of n, a(n) for n=1..20.

FORMULA

a(n) = ((74+47*sqrt(2))*(3-2*sqrt(2))^n+(74-47*sqrt(2))*(3+2*sqrt(2))^n)/4.

G.f.: x*(17-37*x)/(1-6*x+x^2).

PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r2>:=NumberField(x^2-2); S:=[ ((74+47*r2)*(3-2*r2)^n+(74-47*r2)*(3+2*r2)^n)/4: n in [1..20] ]; [ Integers()!S[j]: j in [1..#S] ];

(PARI) {m=20; v=concat([17, 65], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}

CROSSREFS

First trisection of A156567.

Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156568, A156569.

Sequence in context: A130885 A036545 A146807 * A147231 A146815 A216143

Adjacent sequences:  A156567 A156568 A156569 * A156571 A156572 A156573

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Feb 11 2009, Feb 16 2009

EXTENSIONS

G.f. corrected by Klaus Brockhaus, Sep 22 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 30 23:12 EDT 2021. Contains 346365 sequences. (Running on oeis4.)