A163445 - OEIS

%I #9 Sep 08 2022 08:45:46

%S 1,9,79,683,5849,49785,422087,3569323,30132433,254095881,2141117983,

%T 18033145355,151831489769,1278083025081,10757082331991,90529250469067,

%U 761826636963361,6410698145440905,53943922098894703,453912096548803307

%N a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 9.

%C Binomial transform of A163444. Inverse binomial transform of A163446.

%H G. C. Greubel, <a href="/A163445/b163445.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-47).

%F a(n) = ((1+sqrt(2))*(7+sqrt(2))^n + (1-sqrt(2))*(7-sqrt(2))^n)/2.

%F G.f.: (1-5*x)/(1-14*x+47*x^2).

%F E.g.f.: exp(7*x)*( cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Dec 23 2016

%t LinearRecurrence[{14,-47}, {1,9}, 50] (* _G. C. Greubel_, Dec 23 2016 *)

%o (Magma) [ n le 2 select 8*n-7 else 14*Self(n-1)-47*Self(n-2): n in [1..20] ];

%o (PARI) Vec((1-5*x)/(1-14*x+47*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 23 2016

%Y Cf. A163444, A163446.

%K nonn

%O 0,2

%A _Klaus Brockhaus_, Jul 27 2009