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%I #32 Jan 25 2023 07:03:26
%S 2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,512,768,1024,1536,
%T 2048,3072,4096,6144,8192,12288,16384,24576,32768,49152,65536,98304,
%U 131072,196608,262144,393216,524288,786432,1048576,1572864,2097152,3145728
%N a(n) = 2*a(n-2) for n > 2; a(1) = 2, a(2) = 3.
%C Interleaving of A000079 without initial 1 and A007283.
%C Agrees from a(2) onward with A145751 for all terms listed there (up to 65536). Apparently equal to 2, 3 followed by A090989. Equals 2 followed by A163978.
%C Binomial transform is A000129 without first two terms, second binomial transform is A020727, third binomial transform is A164033, fourth binomial transform is A164034, fifth binomial transform is A164035.
%C Number of achiral necklaces or bracelets with n beads using up to 2 colors. For n=5, the eight achiral necklaces or bracelets are AAAAA, AAAAB, AAABB, AABAB, AABBB, ABABB, ABBBB, and BBBBB. - _Robert A. Russell_, Sep 22 2018
%H Vincenzo Librandi, <a href="/A164090/b164090.txt">Table of n, a(n) for n = 1..2000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,2).
%F a(n) = A029744(n+1).
%F a(n) = A052955(n-1) + 1.
%F a(n) = A027383(n-2) + 2 for n > 1.
%F a(n) = A060482(n-1) + 3 for n > 3.
%F a(n) = A070875(n) - A070875(n-1).
%F a(n) = (7 - (-1)^n)*2^((1/4)*(2*n - 1 + (-1)^n))/4.
%F G.f.: x*(2+3*x)/(1-2*x^2).
%F a(n) = A063759(n-1), n>1. - _R. J. Mathar_, Aug 17 2009
%F Sum_{n>=1} 1/a(n) = 5/3. - _Amiram Eldar_, Mar 28 2022
%t a[n_] := If[EvenQ[n], 3*2^(n/2 - 1), 2^((n + 1)/2)]; Array[a, 42] (* _Jean-François Alcover_, Oct 12 2017 *)
%t RecurrenceTable[{a[1]==2,a[2]==3,a[n]==2a[n-2]},a,{n,50}] (* or *) LinearRecurrence[{0,2},{2,3},50] (* _Harvey P. Dale_, Mar 01 2018 *)
%o (Magma) [ n le 2 select n+1 else 2*Self(n-2): n in [1..42] ];
%o (PARI) a(n) = if(n%2,2,3) * 2^((n-1)\2); \\ _Andrew Howroyd_, Oct 07 2017
%Y Cf. A000079 (powers of 2), A007283 (3*2^n), A029744, A145751, A090989, A163978, A000129, A020727, A164033, A164034, A164035, A052955, A027383, A060482, A070875.
%Y Second column of A284855.
%K nonn,easy
%O 1,1
%A _Klaus Brockhaus_, Aug 09 2009
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