%I A007483 M3875
%S A007483 1,5,17,61,217,773,2753,9805,34921,124373,442961,1577629,5618809,
%T A007483 20011685,71272673,253841389,904069513,3219891317,11467812977,
%U A007483 40843221565,145465290649,518082315077,1845177526529,6571697209741
%N A007483 Number of subsequences of [ 1,...,2n+1 ] in which each odd number has 
               an even neighbor.
%C A007483 The even neighbor must differ from the odd number by exactly one.
%D A007483 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007483 R. K. Guy, Moser, William O.J.: Numbers of subsequences without isolated 
               odd members. Fibonacci Quarterly, 34, No. 2, 152-155 (1996). Math. 
               Rev. 97d:11017.
%H A007483 A. Burstein, S. Kitaev and T. Mansour, <a href="http://arXiv.org/abs/
               math.CO/0310379">Independent sets in certain classes of (almost) 
               regular graphs</a>
%F A007483 G.f.: (1+2x)/(1-3x-2x^2). a(n)=3a(n-1)+2a(n-2).
%F A007483 This sequence seems to be generated by the floretion - 0.5'i + 0.5j' 
               + 0.25'ii' + 0.25'jj' - 0.75'kk' + 'ij' - 'ji' - 0.5'jk' - 0.5'ki' 
               - 0.75e ("emseq") - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), 
               Nov 25 2004
%F A007483 a(n)=(3/2+sqrt(17)/2)^n*(1/2+7sqrt(17)/34)+(1/2-7sqrt(17)/34)(3/2-sqrt(17)/
               2)^n - Paul Barry (pbarry(AT)wit.ie), Dec 08 2004
%F A007483 a(n-1) = Sum_{k, 0<=k<=n}2^(n-k)*A122542(n,k), n>=1 . - Philippe DELEHAM 
               (kolotoko(AT)wanadoo.fr), Oct 08 2006
%F A007483 a(n) = upper left term in the 2 X 2 matrix [1,2; 2,2]^(n+1). Also [a(n), 
               a(n+1)] = the 2 X 2 matrix [0,1; 2,3]^(n+1) * [1,1]. Example: [0,
               1; 2,3]^4 * [1,1] = [61, 217]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Mar 16 2008
%Y A007483 Cf. A007482.
%Y A007483 Sequence in context: A146130 A026619 A142956 this_sequence A149662 A149663 
               A149664
%Y A007483 Adjacent sequences: A007480 A007481 A007482 this_sequence A007484 A007485 
               A007486
%K A007483 nonn,easy
%O A007483 0,2
%A A007483 N. J. A. Sloane (njas(AT)research.att.com).