A156161 a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=289, a(2)=7225.

289, 7225, 243049, 8254129, 280395025, 9525174409, 323575532569, 10992042930625, 373405884106369, 12684808016683609, 430910066683134025, 14638257459209870929, 497269843546452475249, 16892536423120174285225

Offset

1,1

Comments

lim_{n -> infinity} a(n)/a(n-1) = (17+12*sqrt(2)).

Links

Table of n, a(n) for n=1..14.

Index entries for linear recurrences with constant coefficients, signature (35,-35,1).

Formula

a(n) = (578+(867-578*sqrt(2))*(17+12*sqrt(2))^n+(867+578*sqrt(2))*(17-12*sqrt(2))^n)/8.

G.f.: x*(289-2890*x+289*x^2)/((1-x)*(1-34*x+x^2)). [corrected by Klaus Brockhaus, Sep 23 2009]

a(1)=289, a(2)=7225, a(3)=243049, a(n) = 35*a(n-1)-35*a(n-2)+a(n-3). - Harvey P. Dale, Dec 11 2013

Example

a(3) = 34*a(2)-a(1)-2312 = 34*7225-289-2312 = 243049.

Mathematica

RecurrenceTable[{a[1]==289, a[2]==7225, a[n]==34a[n-1]-a[n-2]-2312}, a, {n, 20}] (* or *) LinearRecurrence[{35, -35, 1}, {289, 7225, 243049}, 20] (* Harvey P. Dale, Dec 11 2013 *)

Prog

(PARI) {m=14; v=concat([289, 7225], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-2312); v}

Crossrefs

Second trisection of A156159.

Equals 289*A008844. - Klaus Brockhaus, Sep 23 2009

Cf. A156164 (decimal expansion of (17+12*sqrt(2))).

Sequence in context: A332737 A156575 A296404 * A114762 A226747 A260866

Adjacent sequences: A156158 A156159 A156160 * A156162 A156163 A156164

Keyword

nonn

Author

Klaus Brockhaus, Feb 09 2009

Status

approved