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A156157
a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 17, a(2) = 85.
4
17, 85, 493, 2873, 16745, 97597, 568837, 3315425, 19323713, 112626853, 656437405, 3825997577, 22299548057, 129971290765, 757528196533, 4415197888433, 25733659134065, 149986756915957, 874186882361677, 5095134537254105
OFFSET
1,1
COMMENTS
lim_{n -> infinity} a(n)/a(n-1) = 3+2*sqrt(2).
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
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