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A162396 a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 2.

%I A162396 #11 Sep 08 2022 08:45:46
%S A162396 5,2,10,4,20,8,40,16,80,32,160,64,320,128,640,256,1280,512,2560,1024,
%T A162396 5120,2048,10240,4096,20480,8192,40960,16384,81920,32768,163840,65536,
%U A162396 327680,131072,655360,262144,1310720,524288,2621440,1048576,5242880
%N A162396 a(n) = 2*a(n-2) for n > 2; a(1) = 5, a(2) = 2.
%C A162396 Binomial transform is A162268. Fifth binomial transform is A083880 without initial 1.
%H A162396 Vincenzo Librandi, <a href="/A162396/b162396.txt">Table of n, a(n) for n = 1..1000</a>
%H A162396 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,2).
%F A162396 a(n) = (3/2-(-1)^n)*2^(1/4*(2*n+3+(-1)^n)).
%F A162396 G.f.: x*(5+2*x)/(1-2*x^2).
%p A162396 A162396:=n->(3/2-(-1)^n)*2^(1/4*(2*n+3+(-1)^n)): seq(A162396(n), n=1..60); # _Wesley Ivan Hurt_, Oct 08 2017
%t A162396 CoefficientList[Series[(5 + 2*x)/(1 - 2*x^2), {x, 0, 40}], x] (* _Wesley Ivan Hurt_, Oct 08 2017 *)
%t A162396 RecurrenceTable[{a[1]==5, a[2]==2, a[n]==2 a[n-2]}, a, {n, 40}] (* _Vincenzo Librandi_, Oct 09 2017 *)
%o A162396 (Magma) [ n le 2 select 8-3*n else 2*Self(n-2): n in [1..41] ];
%o A162396 (Magma) [Floor((3/2-(-1)^n)*2^(1/4*(2*n+3+(-1)^n))):  n in [1..50]]; // _Vincenzo Librandi_, Oct 09 2017
%Y A162396 Cf. A083880, A162255, A162268.
%K A162396 nonn,easy
%O A162396 1,1
%A A162396 _Klaus Brockhaus_, Jul 02 2009
%E A162396 G.f. corrected, formula simplified, comment added by _Klaus Brockhaus_, Sep 18 2009