A156568 a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=23, a(2)=115.

23, 115, 667, 3887, 22655, 132043, 769603, 4485575, 26143847, 152377507, 888121195, 5176349663, 30169976783, 175843511035, 1024891089427, 5973503025527, 34816127063735, 202923259356883, 1182723429077563

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

Second trisection of A156567. Equals 23*A001653.

Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156569, A156570.

Programs

PARI

{m=19; v=concat([23, 115], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}

Formula

a(n) = 23*((2+sqrt(2))*(3-2*sqrt(2))^n +(2-sqrt(2))*(3+2*sqrt(2))^n)/4.

G.f.: 23*x*(1-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).