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A007484
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Subsequences of [ 1,...,2n+1 ] in which each even number has an odd neighbor.
(Formerly M1767)
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6
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2, 7, 25, 89, 317, 1129, 4021, 14321, 51005, 181657, 646981, 2304257, 8206733, 29228713, 104099605, 370756241, 1320467933, 4702916281, 16749684709, 59654886689, 212464029485, 756701861833, 2695033644469, 9598504657073, 34185581260157, 121753753094617
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Same as Pisot sequence E(2,7)
8*A007484(n) = A007482(n+2) + A007483(n+1) (conjectured, see A104934 for related formula) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Apr 15 2005
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REFERENCES
| R. K. Guy, Moser, William O.J.: Numbers of subsequences without isolated odd members. Fibonacci Quarterly, 34, No. 2, 152-155 (1996).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| a(n) = 3a(n-1) + 2a(n-2).
a(n)=[3/2+(1/2)*sqrt(17)]^n-(4/17)*sqrt(17)*[3/2-(1/2)*sqrt(17)]^n+(4/17)*[3/2+(1/2) *sqrt(17)]^n*sqrt(17)+[3/2-(1/2)*sqrt(17)]^n, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 11 2008
If p[i]=fibonacci(i+2) and if A is the Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)= det A. [From Milan R. Janjic (agnus(AT)blic.net), May 08 2010]
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MAPLE
| A007484 := proc(n) option remember; if n=0 then 2; elif n=1 then 7; else 3*A007484(n-1)+2*A007484(n-2); fi; end;
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CROSSREFS
| Cf. A007455, A007481, A007484.
See A008776 for definitions of Pisot sequences.
Sequence in context: A169651 A030017 A131430 * A070859 A048576 A018907
Adjacent sequences: A007481 A007482 A007483 * A007485 A007486 A007487
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KEYWORD
| easy,nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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