A007972 - OEIS

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

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OFFSET

3,1

LINKS

Sean A. Irvine, Table of n, a(n) for n = 3..100

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

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 *)

CROSSREFS

Cf. A007973, A007974, A007975.

Cf. A000124, A228396, A228397.

Column k=2 of A300003.

Sequence in context: A248538 A248539 A248540 * A248541 A248542 A248543

Adjacent sequences: A007969 A007970 A007971 * A007973 A007974 A007975

KEYWORD

nonn

AUTHOR

J. H. Conway

EXTENSIONS

a(9)-a(41) from Giovanni Resta, Jun 08 2015

Edited by Martin Fuller, Mar 31 2025

STATUS

approved