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A156156 a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 13, a(2) = 53. 4
13, 53, 305, 1777, 10357, 60365, 351833, 2050633, 11951965, 69661157, 406014977, 2366428705, 13792557253, 80388914813, 468540931625, 2730856674937, 15916599117997, 92768738033045, 540695829080273, 3151406236448593 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
lim_{n -> infinity} a(n)/a(n-1) = 3+2*sqrt(2).
LINKS
FORMULA
a(n) = ((50+31*sqrt(2))*(3-2*sqrt(2))^n+(50-31*sqrt(2))*(3+2*sqrt(2))^n)/4.
G.f.: x*(13-25*x)/(1-6*x+x^2).
PROG
(PARI) {m=20; v=concat([13, 53], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}
CROSSREFS
First trisection of A155923.
Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156157, A156158.
Sequence in context: A142188 A248409 A206444 * A201486 A176617 A254895
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

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Last modified July 24 12:16 EDT 2024. Contains 374583 sequences. (Running on oeis4.)