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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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18
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1, 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, 10315944, 15118786
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OFFSET
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0,3
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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).
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LINKS
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FORMULA
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G.f.: -(x^6 - x^5 + x^3 + 2*x^2 - 2*x + 1)/((x^3 + x - 1)*(x-1)^2).
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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 Simon Plouffe in his 1992 dissertation.]
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MATHEMATICA
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CoefficientList[Series[-(x^6 - x^5 + x^3 + 2 x^2 - 2 x + 1)/((x^3 + x - 1) (x - 1)^2), {x, 0, 39}], x] (* Michael De Vlieger, Oct 01 2019 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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