A190974 a(n) = 7*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1.
0, 1, 7, 44, 273, 1691, 10472, 64849, 401583, 2486836, 15399937, 95365379, 590557968, 3657078881, 22646762327, 140241941884, 868459781553, 5378008761451, 33303762422392, 206236293149489, 1277135239934463, 7908765213793796, 48975680296884257
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (7,-5).
Crossrefs
Cf. A190958 (index to generalized Fibonacci sequences).
Programs
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Magma
[n le 2 select n-1 else 7*Self(n-1) - 5*Self(n-2): n in [1..51]]; // G. C. Greubel, Jun 11 2022
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Mathematica
LinearRecurrence[{7,-5}, {0,1}, 50] -
SageMath
[lucas_number1(n,7,5) for n in (0..50)] # G. C. Greubel, Jun 11 2022
Formula
a(n) = ((7/2 + 1/2*sqrt(29))^n - (7/2 - 1/2*sqrt(29))^n)/sqrt(29). - Giorgio Balzarotti, May 28 2011
G.f.: x/(1 - 7*x + 5*x^2). - Philippe Deléham, Oct 12 2011
From G. C. Greubel, Jun 11 2022: (Start)
a(n) = 5^((n-1)/2)*ChebyshevU(n-1, 7/(2*sqrt(5))).
E.g.f.: (2/sqrt(29))*exp(7*x/2)*sinh(sqrt(29)*x/2). (End)