%I A003274 M1583
%S A003274 1,2,6,12,20,34,56,88,136,208,314,470,700,1038,1534,2262,3330,4896,
%T A003274 7192,10558,15492,22724,33324,48860,71630,105002,153912,225594,330650,
%U A003274 484618,710270,1040980,1525660,2235994,3277040,4802768,7038832
%N A003274 Number of key permutations of length n: permutations {a_i} with |a_i-a_{i-1}|=1 
               or 2.
%C A003274 a(n) = 2*A069241(n), n>1.
%D A003274 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003274 S. Avgustinovich and S. Kitaev, On uniquely k-determined permutations, 
               Discr. Math., 308 (2008), 1500-1507.
%D A003274 E. S. Page, Systematic generation of ordered sequences using recurrence 
               relations, Computer J., 14 (1971), 150-153.
%H A003274 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A003274 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A003274 G.f.: x*(-1 + x - 3*x^2 + 2*x^3 - x^5)/((- 1+ x)^2*(-1 + x + x^3)).
%p A003274 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.]
%Y A003274 Sequence in context: A103505 A002378 A005991 this_sequence A121315 A078878 
               A095361
%Y A003274 Adjacent sequences: A003271 A003272 A003273 this_sequence A003275 A003276 
               A003277
%K A003274 nonn
%O A003274 1,2
%A A003274 N. J. A. Sloane (njas(AT)research.att.com).
%E A003274 Better description and g.f. from Erich Friedman (erich.friedman(AT)stetson.edu).