%I #9 Sep 08 2022 08:45:47
%S 1,9,71,539,4041,30169,224911,1675899,12485681,93014729,692919351,
%T 5161913659,38453668921,286460329689,2133983587391,15897089609819,
%U 118425207937761,882207376791049,6571994817093031,48958008011900379
%N a(n) = 10*a(n-1)-19*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
%C Binomial transform of A154235. Inverse binomial transform of A164552.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, -19).
%F a(n) = ((3+2*sqrt(6))*(5+sqrt(6))^n+(3-2*sqrt(6))*(5-sqrt(6))^n)/6.
%F G.f.: (1-x)/(1-10*x+19*x^2).
%t LinearRecurrence[{10,-19},{1,9},30] (* _Harvey P. Dale_, Dec 26 2015 *)
%o (Magma) [ n le 2 select 8*n-7 else 10*Self(n-1)-19*Self(n-2): n in [1..20] ];
%Y Cf. A154235, A164552.
%K nonn
%O 0,2
%A _Klaus Brockhaus_, Aug 15 2009
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