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%I #7 Sep 08 2022 08:45:46
%S 1,9,83,779,7401,70897,682891,6601539,63968273,620798489,6030711171,
%T 58622670907,570089353081,5545446723969,53951697045563,
%U 524954902566899,5108224921291041,49709349684075817,483747874746459571
%N a(n) = 16*a(n-1)-61*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
%C Eighth binomial transform of A108411. Binomial transform of A162758.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16, -61).
%F a(n) = ((3+sqrt(3))*(8+sqrt(3))^n+(3-sqrt(3))*(8-sqrt(3))^n)/6.
%F G.f.: (1-7*x)/(1-16*x+61*x^2).
%t LinearRecurrence[{16,-61},{1,9},30] (* _Harvey P. Dale_, Jan 18 2014 *)
%o (Magma) [ n le 2 select 8*n-7 else 16*Self(n-1)-61*Self(n-2): n in [1..19] ];
%Y Cf. A108411 (powers of 3 repeated), A162758.
%K nonn
%O 0,2
%A _Klaus Brockhaus_, Jul 13 2009