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, 8589935053, 17179869676, 34359738892, 68719477293

Offset

1,1

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

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

a(n) = A062866(n+4,n). - Seiichi Manyama, Apr 23 2026

Mathematica

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

Crossrefs

Cf. A062866, A083706.

Sequence in context: A247438 A132772 A116324 * A044133 A044514 A142110

Adjacent sequences: A179568 A179569 A179570 * A179572 A179573 A179574

Keyword

nonn

Author

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

Status

approved