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A003274 Number of key permutations of length n: permutations {a_i} with |a_i-a_{i-1}|=1 or 2.
(Formerly M1583)
14
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; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

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.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

R. H. Hardin, Table of n, a(n) for n=1..251, May 06 2010

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

FORMULA

For n>1, a(n) = 2*A069241(n).

G.f.: x*(-1 + x - 3*x^2 + 2*x^3 - x^5)/((- 1+ x)^2*(-1 + x + x^3)).

MAPLE

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.]

CROSSREFS

Sequence in context: A005991 A194110 A184432 * A121315 A078878 A095361

Adjacent sequences:  A003271 A003272 A003273 * A003275 A003276 A003277

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Better description and g.f. from Erich Friedman.

STATUS

approved

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Last modified December 21 17:16 EST 2014. Contains 252324 sequences.