A163461 - OEIS

%I #10 Sep 08 2022 08:45:46

%S 1,10,101,1028,10525,108238,1116809,11551760,119703769,1242078802,

%T 12900820685,134090546972,1394465011381,14507216994070,

%U 150967169994161,1571338917363368,16357694083001905,170302719022328218

%N a(n) = 18*a(n-1) - 79*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

%C Binomial transform of A163460. Inverse binomial transform of A163462.

%H G. C. Greubel, <a href="/A163461/b163461.txt">Table of n, a(n) for n = 0..975</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18, -79).

%F a(n) = ((2+sqrt(2))*(9+sqrt(2))^n + (2-sqrt(2))*(9-sqrt(2))^n)/4.

%F G.f.: (1-8*x)/(1-18*x+79*x^2).

%F 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

%t LinearRecurrence[{18,-79},{1,10},30] (* _Harvey P. Dale_, Jul 25 2013 *)

%o (Magma) [ n le 2 select 9*n-8 else 18*Self(n-1)-79*Self(n-2): n in [1..18] ];

%o (PARI) Vec((1-8*x)/(1-18*x+79*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 24 2016

%Y Cf. A163460, A163462.

%K nonn

%O 0,2

%A _Klaus Brockhaus_, Jul 28 2009