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 A154239 a(n) = ( (7 + sqrt(6))^n - (7 - sqrt(6))^n )/(2*sqrt(6)). 1
 1, 14, 153, 1540, 14981, 143514, 1365013, 12939080, 122451561, 1157941414, 10945762673, 103449196620, 977620957741, 9238377953714, 87299590169133, 824944010358160, 7795333767741521, 73662080302980414, 696069772228840393 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS lim_{n -> infinity} a(n)/a(n-1) = 7 + sqrt(6) = 9.4494897427.... LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (14, -43). FORMULA From Philippe Deléham, Jan 06 2009: (Start) a(n) = 14*a(n-1) - 43*a(n-2)for n>1, with a(0)=0, a(1)=1. G.f.: x/(1 - 14x + 43x^2). (End) E.g.f.: sinh(sqrt(6)*x)*exp(7*x)/sqrt(6). - Ilya Gutkovskiy, Sep 07 2016 MATHEMATICA Join[{a=1, b=14}, Table[c=14*b-43*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *) LinearRecurrence[{14, -43}, {1, 14}, 25] (* or *) Table[( (7 + sqrt(6))^n - (7 - sqrt(6))^n )/(2*sqrt(6)), {n, 1, 25}] (* G. C. Greubel, Sep 07 2016 *) PROG (Magma) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-6); S:=[ ((7+r)^n-(7-r)^n)/(2*r): n in [1..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 07 2009 I:=[1, 14]; [n le 2 select I[n] else 14*Self(n-1)-43*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Sep 07 2016 CROSSREFS Cf. A010464 (decimal expansion of square root of 6). Sequence in context: A222677 A016163 A153884 * A016215 A329711 A290675 Adjacent sequences: A154236 A154237 A154238 * A154240 A154241 A154242 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Jan 05 2009 EXTENSIONS Extended beyond a(7) by Klaus Brockhaus, Jan 07 2009 Edited by Klaus Brockhaus, Oct 06 2009 STATUS approved

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Last modified December 4 21:08 EST 2023. Contains 367565 sequences. (Running on oeis4.)