A163308 a(n) = 16*a(n-1) - 59*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
1, 9, 85, 829, 8249, 83073, 842477, 8578325, 87547057, 894631737, 9148831429, 93598030381, 957787431785, 9802315116081, 100327583381981, 1026904742262917, 10511148456669793, 107590995513204585
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..985
- Index entries for linear recurrences with constant coefficients, signature (16, -59).
Programs
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Magma
[ n le 2 select 8*n-7 else 16*Self(n-1)-59*Self(n-2): n in [1..18] ];
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Mathematica
LinearRecurrence[{16,-59},{1,9},20] (* Harvey P. Dale, Dec 06 2013 *) -
PARI
Vec((1-7*x)/(1-16*x+59*x^2) + O(x^50)) \\ G. C. Greubel, Dec 18 2016
Formula
a(n) = ((5+sqrt(5))*(8+sqrt(5))^n + (5-sqrt(5))*(8-sqrt(5))^n)/10.
G.f.: (1-7*x)/(1-16*x+59*x^2).
E.g.f.: (1/5)*exp(8*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - G. C. Greubel, Dec 18 2016
Comments