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%I #25 Sep 08 2022 08:45:47
%S 1,5,13,41,121,365,1093,3281,9841,29525,88573,265721,797161,2391485,
%T 7174453,21523361,64570081,193710245,581130733,1743392201,5230176601,
%U 15690529805,47071589413,141214768241,423644304721,1270932914165
%N a(n) = (3*3^n-(-1)^n)/2.
%C Interleaving of A096053 and A083884 without initial term 1.
%C Partial sums are (essentially) in A080926.
%C First differences are (essentially) in A105723.
%C a(n)+a(n+1) = A008776(n+1) = A099856(n+1) = A110593(n+2).
%C Binomial transform of A056450. Inverse binomial transform of A164908.
%H Vincenzo Librandi, <a href="/A164907/b164907.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,3).
%F a(n) = 2*a(n-1)+3*a(n-2) for n > 1; a(0) = 1, a(1) = 5.
%F G.f.: (1+3*x)/((1+x)*(1-3*x)).
%F a(n) = 3*a(n-1)+2*(-1)^n. - _Carmine Suriano_, Mar 21 2014
%p A164907:=n->(3*3^n - (-1)^n)/2; seq(A164907(n), n=0..30); # _Wesley Ivan Hurt_, Mar 21 2014
%t Table[(3*3^n - (-1)^n)/2, {n, 0, 30}] (* _Wesley Ivan Hurt_, Mar 21 2014 *)
%t LinearRecurrence[{2,3},{1,5},50] (* _Harvey P. Dale_, Oct 31 2018 *)
%o (Magma) [ (3*3^n-(-1)^n)/2: n in [0..25] ];
%Y Equals A046717 without initial term 1 and A080925 without initial term 0. Equals A084182 / 2 from second term onward.
%Y Cf. A096053, A083884, A080926, A105723, A008776, A099856, A110593, A056450, A164908.
%K nonn,easy
%O 0,2
%A _Klaus Brockhaus_, Aug 31 2009
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