A163461 a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
1, 10, 101, 1028, 10525, 108238, 1116809, 11551760, 119703769, 1242078802, 12900820685, 134090546972, 1394465011381, 14507216994070, 150967169994161, 1571338917363368, 16357694083001905, 170302719022328218
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..975
- Index entries for linear recurrences with constant coefficients, signature (18, -79).
Programs
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Magma
[ n le 2 select 9*n-8 else 18*Self(n-1)-79*Self(n-2): n in [1..18] ];
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Mathematica
LinearRecurrence[{18,-79},{1,10},30] (* Harvey P. Dale, Jul 25 2013 *) -
PARI
Vec((1-8*x)/(1-18*x+79*x^2) + O(x^50)) \\ G. C. Greubel, Dec 24 2016
Formula
a(n) = ((2+sqrt(2))*(9+sqrt(2))^n + (2-sqrt(2))*(9-sqrt(2))^n)/4.
G.f.: (1-8*x)/(1-18*x+79*x^2).
E.g.f.: (1/2)*exp(9*x)*(2*cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x)). - G. C. Greubel, Dec 24 2016
Comments