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%I #14 May 26 2016 15:53:22
%S 31,66,134,267,529,1048,2080,4137,8243,16446,32842,65623,131173,
%T 262260,524420,1048725,2097319,4194490,8388814,16777443,33554681,
%U 67109136,134218024,268435777,536871259,1073742198,2147484050,4294967727
%N Number of permutations of 1..n+4 with the number moved left exceeding the number moved right by n.
%C Recurrence would also extend to an a(0) if the definition were made to exclude the identity permutation.
%H R. H. Hardin, <a href="/A179571/b179571.txt">Table of n, a(n) for n = 1..99</a>
%F Empirical: a(n)=5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4) ; G.f.: -x*(-31+89*x-83*x^2+26*x^3) / ( (2*x-1)*(x-1)^3 ).
%F Empirical: a(n) = (n^2+3*n-6)/2 +2^(n+4) = 2^(n+4)+A046691(n-1). - _R. J. Mathar_, May 26 2016
%t Drop[Accumulate[Table[BitSet[n, (n + 2)], {n, 0, 100}]], 2] (* _Vladimir Joseph Stephan Orlovsky_, Jul 19 2011 *)
%Y Cf. A083706.
%K nonn
%O 1,1
%A _R. H. Hardin_, g.f. from _R. J. Mathar_ in the Sequence Fans Mailing List, Jul 19 2010