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%I #15 Jul 31 2023 16:41:26
%S 1,9,21,69,201,609,1821,5469,16401,49209,147621,442869,1328601,
%T 3985809,11957421,35872269,107616801,322850409,968551221,2905653669,
%U 8716961001,26150883009,78452649021,235357947069,706073841201,2118221523609,6354664570821,19063993712469
%N a(n) = 2*a(n-1) + 3*a(n-2), with a(0) = 1, a(1) = 9.
%H Andrew Howroyd, <a href="/A137340/b137340.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 (2,3).
%F G.f.: (1 + 7*x)/((1 + x)*(1 - 3*x)). - _Andrew Howroyd_, Feb 02 2020
%F From _Klaus Purath_, Mar 10 2021: (Start)
%F a(n) = (5*3^n - 3*(-1)^n)/2.
%F a(2*n) = (5*9^n - 3)/2.
%F a(2*n+1) = (15*9^n + 3)/2.
%F a(n) = 20*3^(n-2) + a(n-2), n > 1.
%F a(n) = A096019(n) - 2*(-1)^n. (End)
%t LinearRecurrence[{2,3},{1,9},30] (* _Harvey P. Dale_, Jul 31 2023 *)
%o (PARI) Vec((1 + 7*x)/((1 + x)*(1 - 3*x)) + O(x^40)) \\ _Andrew Howroyd_, Feb 02 2020
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Apr 21 2008
%E Terms a(10) and beyond from _Andrew Howroyd_, Feb 02 2020
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