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Search: id:A007483
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| A007483 |
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Number of subsequences of [ 1,...,2n+1 ] in which each odd number has an even neighbor.
(Formerly M3875)
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+0
8
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| 1, 5, 17, 61, 217, 773, 2753, 9805, 34921, 124373, 442961, 1577629, 5618809, 20011685, 71272673, 253841389, 904069513, 3219891317, 11467812977, 40843221565, 145465290649, 518082315077, 1845177526529, 6571697209741
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The even neighbor must differ from the odd number by exactly one.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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.
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LINKS
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A. Burstein, S. Kitaev and T. Mansour, Independent sets in certain classes of (almost) regular graphs
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FORMULA
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G.f.: (1+2x)/(1-3x-2x^2). a(n)=3a(n-1)+2a(n-2).
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
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
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
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
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CROSSREFS
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Cf. A007482.
Adjacent sequences: A007480 A007481 A007482 this_sequence A007484 A007485 A007486
Sequence in context: A146130 A026619 A142956 this_sequence A149662 A149663 A149664
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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