A156162 a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=625, a(2)=18769.

625, 18769, 635209, 21576025, 732947329, 24898630849, 845820499225, 28732998340489, 976076123075089, 33157855186210225, 1126391000208070249, 38264136151888175929, 1299854238163989909025, 44156779961423768728609

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+(387-182*sqrt(2))*(17+12*sqrt(2))^n+(387+182*sqrt(2))*(17-12*sqrt(2))^n)/8.

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

Example

a(3) = 34*a(2)-a(1)-2312 = 34*18769-625-2312 = 635209.

Mathematica

RecurrenceTable[{a[1]==625, a[2]==18769, a[n]==34a[n-1]-a[n-2]-2312}, a, {n, 20}] (* or *) LinearRecurrence[{35, -35, 1}, {625, 18769, 635209}, 20] (* Harvey P. Dale, Sep 29 2016 *)

Prog

(PARI) {m=14; v=concat([625 , 18769], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-2312); v}

Crossrefs

Third trisection of A156159.

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

Sequence in context: A055868 A016852 A016972 * A017044 A080175 A017128

Adjacent sequences: A156159 A156160 A156161 * A156163 A156164 A156165

Keyword

nonn

Author

Klaus Brockhaus, Feb 09 2009

Extensions

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

Status

approved