A081575 Fifth binomial transform of Fibonacci numbers F(n).
0, 1, 11, 92, 693, 4955, 34408, 234793, 1584891, 10624804, 70911005, 471901739, 3134499984, 20794349393, 137837343787, 913174649260, 6047638172037, 40041955063867, 265079998713464, 1754663288995961, 11613976216265115
Offset: 0
References
- S. Falcon, Iterated Binomial Transforms of the k-Fibonacci Sequence, British Journal of Mathematics & Computer Science, 4 (22): 2014.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- S. Falcon, Iterated Binomial Transforms of the k-Fibonacci Sequence, British Journal of Mathematics & Computer Science, 4 (22): 2014.
- Index entries for linear recurrences with constant coefficients, signature (11,-29).
Programs
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GAP
a:=[0,1];; for n in [3..30] do a[n]:=11*a[n-1]-29*a[n-2]; od; a; # G. C. Greubel, Aug 13 2019
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Magma
[n le 2 select (n-1) else 11*Self(n-1)-29*Self(n-2): n in [1..25]]; // Vincenzo Librandi, Aug 09 2013
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Maple
seq(coeff(series(x/(1-11*x+29*x^2), x, n+1), x, n), n = 0..30); # G. C. Greubel, Aug 13 2019
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Mathematica
LinearRecurrence[{11,-29}, {0,1}, 30] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2011; modified by G. C. Greubel, Aug 13 2019 *) CoefficientList[Series[x/(1 -11x +29x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 09 2013 *) -
PARI
my(x='x+O('x^30)); Vec(x/(1-11*x+29*x^2)) \\ G. C. Greubel, Aug 13 2019 -
Sage
[lucas_number1(n,11,29) for n in range(0, 21)] # Zerinvary Lajos, Apr 27 2009
Formula
a(n) = 11*a(n-1) - 29*a(n-2), a(0)=0, a(1)=1.
a(n) = ((sqrt(5)/2 + 11/2)^n - (11/2 - sqrt(5)/2)^n)/sqrt(5).
G.f.: x/(1 - 11*x + 29*x^2). - adapted by Vincenzo Librandi, Aug 09 2013
E.g.f.: 2*exp(11*x/2)*sinh(sqrt(5)*x/2)/sqrt(5). - Ilya Gutkovskiy, Aug 12 2017
Comments