A179571 Number of permutations of 1..n+4 with the number moved left exceeding the number moved right by n.

31, 66, 134, 267, 529, 1048, 2080, 4137, 8243, 16446, 32842, 65623, 131173, 262260, 524420, 1048725, 2097319, 4194490, 8388814, 16777443, 33554681, 67109136, 134218024, 268435777, 536871259, 1073742198, 2147484050, 4294967727

Offset: 1

Author

R. H. Hardin, g.f. from R. J. Mathar in the Sequence Fans Mailing List, Jul 19 2010

Keywords

• nonn

Comments

Recurrence would also extend to an a(0) if the definition were made to exclude the identity permutation.

Links

• R. H. Hardin, Table of n, a(n) for n = 1..99

Crossrefs

Cf. A083706.

Programs

Mathematica

Drop[Accumulate[Table[BitSet[n, (n + 2)], {n, 0, 100}]], 2] (* Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *)

Formula

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 ).

Empirical: a(n) = (n^2+3*n-6)/2 +2^(n+4) = 2^(n+4)+A046691(n-1). - R. J. Mathar, May 26 2016