A156160 a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=169, a(2)=2809.

169, 2809, 93025, 3157729, 107267449, 3643933225, 123786459889, 4205095700689, 142849467361225, 4852676794578649, 164848161548310529, 5599984815847977025, 190234635577282906009, 6462377624811770824969

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+ (2211-1550*sqrt(2))*(17+12*sqrt(2))^n+(2211+1550*sqrt(2))*(17-12*sqrt(2))^n)/8.

G.f.: x*(169-3106*x+625*x^2)/((1-x)*(1-34*x+x^2)).

Example

a(3) = 34*a(2)-a(1)-2312 = 34*2809-169-2312 = 93025.

Mathematica

LinearRecurrence[{35, -35, 1}, {169, 2809, 93025}, 20] (* Harvey P. Dale, Nov 15 2014 *)

Prog

(PARI) {m=14; v=concat([169, 2809], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-2312); v}

Crossrefs

First trisection of A156159.

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

Sequence in context: A183716 A012014 A221889 * A264261 A232002 A220679

Adjacent sequences: A156157 A156158 A156159 * A156161 A156162 A156163

Keyword

nonn

Author

Klaus Brockhaus, Feb 09 2009

Extensions

G.f. corrected by Klaus Brockhaus, Sep 23 2009

Status

approved