A156569 a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=37, a(2)=205.

37, 205, 1193, 6953, 40525, 236197, 1376657, 8023745, 46765813, 272571133, 1588660985, 9259394777, 53967707677, 314546851285, 1833313400033, 10685333548913, 62278687893445, 362986793811757, 2115642074977097

Offset: 1

Author

Klaus Brockhaus, Feb 11 2009, Feb 16 2009

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (6,-1).

Crossrefs

Third trisection of A156567.

Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156568, A156570.

Programs

Mathematica

LinearRecurrence[{6,-1},{37,205},30] (* Harvey P. Dale, Aug 18 2014 *)

PARI

{m=19; v=concat([37, 205], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}

Formula

a(n) = ((34+7*sqrt(2))*(3-2*sqrt(2))^n+(34-7*sqrt(2))*(3+2*sqrt(2))^n)/4.

G.f.: x*(37-17*x)/(1-6*x+x^2). [corrected by Klaus Brockhaus, Sep 22 2009]

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