A163445 a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
1, 9, 79, 683, 5849, 49785, 422087, 3569323, 30132433, 254095881, 2141117983, 18033145355, 151831489769, 1278083025081, 10757082331991, 90529250469067, 761826636963361, 6410698145440905, 53943922098894703, 453912096548803307
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (14,-47).
Programs
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Magma
[ n le 2 select 8*n-7 else 14*Self(n-1)-47*Self(n-2): n in [1..20] ];
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Mathematica
LinearRecurrence[{14,-47}, {1,9}, 50] (* G. C. Greubel, Dec 23 2016 *) -
PARI
Vec((1-5*x)/(1-14*x+47*x^2) + O(x^50)) \\ G. C. Greubel, Dec 23 2016
Formula
a(n) = ((1+sqrt(2))*(7+sqrt(2))^n + (1-sqrt(2))*(7-sqrt(2))^n)/2.
G.f.: (1-5*x)/(1-14*x+47*x^2).
E.g.f.: exp(7*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Dec 23 2016
Comments