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 A156569 a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=37, a(2)=205. 3
 37, 205, 1193, 6953, 40525, 236197, 1376657, 8023745, 46765813, 272571133, 1588660985, 9259394777, 53967707677, 314546851285, 1833313400033, 10685333548913, 62278687893445, 362986793811757, 2115642074977097 (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 Index entries for linear recurrences with constant coefficients, signature (6,-1). FORMULA a(n) = ((34+7*sqrt(2))*(3-2*sqrt(2))^n+(34-7*sqrt(2))*(3+2*sqrt(2))^n)/4. G.f.: x*(37-17*x)/(1-6*x+x^2). MATHEMATICA LinearRecurrence[{6, -1}, {37, 205}, 30] (* Harvey P. Dale, Aug 18 2014 *) PROG (PARI) {m=19; v=concat([37, 205], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v} CROSSREFS Third trisection of A156567. Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156568, A156570. Sequence in context: A211754 A211765 A221888 * A141984 A327033 A052166 Adjacent sequences:  A156566 A156567 A156568 * A156570 A156571 A156572 KEYWORD nonn,easy AUTHOR Klaus Brockhaus, Feb 11 2009, Feb 16 2009 EXTENSIONS G.f. corrected by Klaus Brockhaus, Sep 22 2009 STATUS approved

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Last modified July 25 08:21 EDT 2021. Contains 346285 sequences. (Running on oeis4.)