A156157 a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 17, a(2) = 85.

17, 85, 493, 2873, 16745, 97597, 568837, 3315425, 19323713, 112626853, 656437405, 3825997577, 22299548057, 129971290765, 757528196533, 4415197888433, 25733659134065, 149986756915957, 874186882361677, 5095134537254105

Offset: 1

Author

Klaus Brockhaus, Feb 09 2009

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Second trisection of A155923. Equals 17*A001653.

Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156156, A156158.

Programs

PARI

{m=20; v=concat([17, 85], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}

Formula

a(n) = ((2+sqrt(2))*(3-2*sqrt(2))^n+(2-sqrt(2))*(3+2*sqrt(2))^n)*17/4.

G.f.: 17*x*(1-x)/(1-6*x+x^2).

Extensions

Replaced abbreviation by sqrt(2) Klaus Brockhaus, Feb 12 2009

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