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Search: id:A007382
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| A007382 |
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Number of strict (-1)st-order maximal independent sets in path graph.
(Formerly M2365)
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+0
2
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| 0, 0, 3, 4, 11, 16, 32, 49, 87, 137, 231, 369, 608, 978, 1595, 2574, 4179, 6754, 10944, 17699, 28655, 46355, 75023, 121379, 196416, 317796, 514227, 832024, 1346267
(list; graph; listen)
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OFFSET
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1,3
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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. Yanco and A. Bagchi, ``K-th order maximal independent sets in path and cycle graphs,'' J. Graph Theory, submitted, 1994.
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FORMULA
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John W. Layman (layman(AT)math.vt.edu) observes that if b(n)=1+A007382(n) then b(n) = b(n-1) + 3b(n-2) - 2b(n-3) - 3b(n-4) + b(n-5) + b(n-6) for all 27 terms shown.
G.f.: [x^3(x^3+2x^2-x-3)]/[(1-x-x^2)*(1-x^2)^2].
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CROSSREFS
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Equals A054451(n+1) - 1.
Sequence in context: A041020 A041527 A001641 this_sequence A127804 A027306 A026676
Adjacent sequences: A007379 A007380 A007381 this_sequence A007383 A007384 A007385
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Mira Bernstein
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