A156157 - OEIS

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

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OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..20.

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

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).

PROG

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

CROSSREFS

Second trisection of A155923. Equals 17*A001653.

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

Sequence in context: A156968 A212487 A288420 * A146389 A328010 A041554

Adjacent sequences: A156154 A156155 A156156 * A156158 A156159 A156160

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Feb 09 2009

EXTENSIONS

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

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

STATUS

approved