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A163309 a(n) = 18*a(n-1) - 76*a(n-2) for n > 1; a(0) = 1, a(1) = 10. 3

%I

%S 1,10,104,1112,12112,133504,1482560,16539776,185041408,2073722368,

%T 23263855616,261146501120,2932583993344,32939377795072,

%U 370032416817152,4157190790283264,46706970546995200,524778969784385536

%N a(n) = 18*a(n-1) - 76*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

%C Binomial transform of A163308. Inverse binomial transform of A163310.

%H G. C. Greubel, <a href="/A163309/b163309.txt">Table of n, a(n) for n = 0..950</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-76).

%F a(n) = ((5+sqrt(5))*(9+sqrt(5))^n + (5-sqrt(5))*(9-sqrt(5))^n)/10.

%F G.f.: (1-8*x)/(1-18*x+76*x^2).

%F E.g.f.: (1/5)*exp(9*x)*(5*cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x)). - _G. C. Greubel_, Dec 18 2016

%t LinearRecurrence[{18,-76}, {1,10}, 50] (* _G. C. Greubel_, Dec 18 2016 *)

%o (MAGMA) [ n le 2 select 9*n-8 else 18*Self(n-1)-76*Self(n-2): n in [1..18] ];

%o (PARI) Vec((1-8*x)/(1-18*x+76*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 18 2016

%Y Cf. A163308, A163310.

%K nonn

%O 0,2

%A _Klaus Brockhaus_, Jul 24 2009

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Last modified May 6 17:00 EDT 2021. Contains 343586 sequences. (Running on oeis4.)