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%I #12 Apr 22 2024 09:42:11
%S 1,9,69,501,3561,25089,176109,1234221,8643921,60520569,423683349,
%T 2965901541,20761665081,145332718449,1017332217789,7121335090461,
%U 49849374331041,348945706410729,2442620203155429,17098342196928981
%N a(n) = (3*7^n-3^n)/2.
%C Partial sums are in A016138.
%C Binomial transform of A016129. Inverse binomial transform of A165148.
%H Vincenzo Librandi, <a href="/A165147/b165147.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-21).
%F a(n) = 10*a(n-1)-21*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
%F G.f.: (1-x)/((1-3*x)*(1-7*x)).
%t LinearRecurrence[{10, -21}, {1, 9}, 25] (* _Paolo Xausa_, Apr 22 2024 *)
%o (Magma) [ (3*7^n-3^n)/2: n in [0..19] ];
%Y Cf. A016138, A016129, A165148.
%K nonn,easy
%O 0,2
%A _Klaus Brockhaus_, Sep 15 2009