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 A156158 a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 25, a(2) = 137. 4
 25, 137, 797, 4645, 27073, 157793, 919685, 5360317, 31242217, 182092985, 1061315693, 6185801173, 36053491345, 210135146897, 1224757390037, 7138409193325, 41605697769913, 242495777426153, 1413368966787005 (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) = ((26+7*sqrt(2))*(3-2*sqrt(2))^n+(26-7*sqrt(2))*(3+2*sqrt(2))^n)/4. G.f.: x*(25-13*x)/(1-6*x+x^2). MATHEMATICA LinearRecurrence[{6, -1}, {25, 137}, 30] (* Harvey P. Dale, Jan 02 2019 *) PROG (PARI) {m=19; v=concat([25, 137], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v} CROSSREFS Third trisection of A155923. Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156156, A156157. Sequence in context: A305956 A317217 A147489 * A195977 A233368 A240415 Adjacent sequences:  A156155 A156156 A156157 * A156159 A156160 A156161 KEYWORD nonn,easy 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 May 25 07:08 EDT 2020. Contains 334584 sequences. (Running on oeis4.)