A154340 a(n) = ( (5 + 2*sqrt(2))^n - (5 - 2*sqrt(2))^n )/(4*sqrt(2)).
1, 10, 83, 660, 5189, 40670, 318487, 2493480, 19520521, 152816050, 1196311643, 9365243580, 73315137869, 573942237830, 4493065034527, 35173632302160, 275354217434641, 2155590425209690, 16874882555708003, 132103788328515300
Offset: 1
Links
- G. C. Greubel, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (10, -17).
Programs
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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 -
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
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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
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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 *) -
PARI
a(n)=([0,1; -17,10]^(n-1)*[1;10])[1,1] \\ Charles R Greathouse IV, Sep 12 2016
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Sage
[lucas_number1(n,10,17) for n in range(1, 30)] # Zerinvary Lajos, Apr 26 2009
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
Extensions
Extended beyond a(7) by Klaus Brockhaus, Jan 12 2009
Edited by Klaus Brockhaus, Oct 08 2009
Comments