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Search: id:A003274
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| A003274 |
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Number of key permutations of length n: permutations {a_i} with |a_i-a_{i-1}|=1 or 2.
(Formerly M1583)
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+0
4
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| 1, 2, 6, 12, 20, 34, 56, 88, 136, 208, 314, 470, 700, 1038, 1534, 2262, 3330, 4896, 7192, 10558, 15492, 22724, 33324, 48860, 71630, 105002, 153912, 225594, 330650, 484618, 710270, 1040980, 1525660, 2235994, 3277040, 4802768, 7038832
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n) = 2*A069241(n), n>1.
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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).
S. Avgustinovich and S. Kitaev, On uniquely k-determined permutations, Discr. Math., 308 (2008), 1500-1507.
E. S. Page, Systematic generation of ordered sequences using recurrence relations, Computer J., 14 (1971), 150-153.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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G.f.: x*(-1 + x - 3*x^2 + 2*x^3 - x^5)/((- 1+ x)^2*(-1 + x + x^3)).
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MAPLE
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A003274:=-(1-z+3*z**2-2*z**3+z**5)/(z**3+z-1)/(z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A103505 A002378 A005991 this_sequence A121315 A078878 A095361
Adjacent sequences: A003271 A003272 A003273 this_sequence A003275 A003276 A003277
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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).
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EXTENSIONS
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Better description and g.f. from Erich Friedman (erich.friedman(AT)stetson.edu).
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