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 A154340 a(n) = ( (5 + 2*sqrt(2))^n - (5 - 2*sqrt(2))^n )/(4*sqrt(2)). 1
 1, 10, 83, 660, 5189, 40670, 318487, 2493480, 19520521, 152816050, 1196311643, 9365243580, 73315137869, 573942237830, 4493065034527, 35173632302160, 275354217434641, 2155590425209690, 16874882555708003, 132103788328515300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS First differences are in A164588. Lim_{n -> infinity} a(n)/a(n-1) = 5 + 2*sqrt(2) = 7.8284271247.... LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (10, -17). FORMULA a(n) = 10*a(n-1) - 17*a(n-2) for n > 1, with a(0)=0, a(1)=1. - Philippe Deléham, Jan 12 2009 G.f.: x/(1 - 10*x + 17*x^2). - Klaus Brockhaus, Jan 12 2009, corrected Oct 08 2009 E.g.f.: (1/sqrt(8))*exp(5*x)*sinh(2*sqrt(2)*x). - G. C. Greubel, Sep 11 2016 MAPLE A154340:=n->((5+2*sqrt(2))^n-(5-2*sqrt(2))^n)/(4*sqrt(2)): seq(simplify(A154340(n)), n=1..30); # Wesley Ivan Hurt, Sep 12 2016 MATHEMATICA Drop[CoefficientList[Series[x/(1-10*x+17*x^2), {x, 0, 30}], x], 1] (* Vladimir Joseph Stephan Orlovsky, Jan 27 2011, modified by G. C. Greubel, Jun 01 2019 *) LinearRecurrence[{10, -17}, {1, 10}, 30] (* or *) Table[Simplify[((5 + 2*Sqrt[2])^n -(5-2*Sqrt[2])^n)/(4*Sqrt[2])], {n, 1, 30}] (* G. C. Greubel, Sep 11 2016 *) PROG (MAGMA) Z:=PolynomialRing(Integers()); N:=NumberField(x^2-2); S:=[ ((5+2*r)^n-(5-2*r)^n)/(4*r): n in [1..30] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jan 12 2009 (Sage) [lucas_number1(n, 10, 17) for n in range(1, 30)] # Zerinvary Lajos, Apr 26 2009 (MAGMA) I:=[1, 10]; [n le 2 select I[n] else 10*Self(n-1)-17*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Sep 12 2016 (PARI) a(n)=([0, 1; -17, 10]^(n-1)*[1; 10])[1, 1] \\ Charles R Greathouse IV, Sep 12 2016 CROSSREFS Cf. A002193 (decimal expansion of sqrt(2)), A164588. Sequence in context: A238843 A026954 A116879 * A037699 A037608 A055149 Adjacent sequences:  A154337 A154338 A154339 * A154341 A154342 A154343 KEYWORD nonn,easy AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009 EXTENSIONS Extended beyond a(7) by Klaus Brockhaus, Jan 12 2009 Edited by Klaus Brockhaus, Oct 08 2009 STATUS approved

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Last modified May 12 19:15 EDT 2021. Contains 343829 sequences. (Running on oeis4.)