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a(n) = 12*a(n-1)-30*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
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%I #9 Sep 08 2022 08:45:47

%S 1,10,90,780,6660,56520,478440,4045680,34194960,288969120,2441780640,

%T 20632294080,174334109760,1473040494720,12446462643840,

%U 105166336884480,888602163298560,7508235853048320,63440765337623040,536042108460026880

%N a(n) = 12*a(n-1)-30*a(n-2) for n > 1; a(0) = 1, a(1) = 10.

%C Binomial transform of A164551. Inverse binomial transform of A164553.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12, -30).

%F a(n) = ((3+2*sqrt(6))*(6+sqrt(6))^n+(3-2*sqrt(6))*(6-sqrt(6))^n)/6.

%F G.f.: (1-2*x)/(1-12*x+30*x^2).

%t LinearRecurrence[{12,-30},{1,10},20] (* _Harvey P. Dale_, Apr 19 2019 *)

%o (Magma) [ n le 2 select 9*n-8 else 12*Self(n-1)-30*Self(n-2): n in [1..20] ];

%Y Cf. A164551, A164553.

%K nonn

%O 0,2

%A _Klaus Brockhaus_, Aug 15 2009