A007972 Number of permutations that are 2 "block reversals" away from 12...n.
2, 15, 52, 129, 266, 487, 820, 1297, 1954, 2831, 3972, 5425, 7242, 9479, 12196, 15457, 19330, 23887, 29204, 35361, 42442, 50535, 59732, 70129, 81826, 94927, 109540, 125777, 143754, 163591, 185412, 209345, 235522, 264079, 295156, 328897, 365450, 404967, 447604
Offset: 3
Keywords
Links
- Sean A. Irvine, Table of n, a(n) for n = 3..100
Programs
-
Mathematica
a[n_] := Block[{s, allb, r = Flatten[Table[{i, j}, {i, n}, {j, i + 1, n}], 1]}, allb[pp_] := Union@ Table[ s=pp; s[[Range @@ e]] = Reverse[ s[[ Range @@ e]]]; s, {e, r}]; Length[Flatten[allb /@ allb[Range[n]], 1] // Union] - 1]; a /@ Range[3,15] (* Giovanni Resta, Jun 08 2015 *)
Formula
a(n) = (n^4+6*n^3+11*n^2-12*n+6)/6 (conjectured). - Giovanni Resta, Jun 08 2015
Conjectured g.f.: (-2-5x+3x^2+x^3-x^4)/(-1+x)^5. - Benedict W. J. Irwin, Feb 20 2016
a(n) = A228396(n) - A000124(n-1). See C. Homberger links from A228396. This proves the above conjectured formulas up to offset. - Martin Fuller, Mar 31 2025
Extensions
a(9)-a(41) from Giovanni Resta, Jun 08 2015
Edited by Martin Fuller, Mar 31 2025