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A164907 a(n) = (3*3^n-(-1)^n)/2.

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