A334412 Number of ordered pairs of permutations of [n] avoiding synchronous double descent pairs.
1, 1, 4, 35, 545, 13250, 463899, 22106253, 1375915620, 108386009099, 10540705282001, 1240370638524842, 173704235075714947, 28549174106487593365, 5441843626292088857818, 1190762128123996264128849, 296456799935194225886732961, 83321234634397591315509479058
Offset: 0
Keywords
Examples
a(3) = (3!)^2 - 1 = 35: only (321,321) does not avoid synchronous double descent pairs among the ordered pairs of permutations of [3].
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..100
- Wikipedia, Permutation
Programs
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Maple
b:= proc(n, u, v, t) option remember; `if`(n=0, 1, add(add( b(n-1, sort([u-j, v-i])[], 1), i=1..v)+add( b(n-1, sort([u-j, v+i-1])[], 1), i=1..n-v), j=1..u)+add(add( b(n-1, sort([u+j-1, v-i])[], 1), i=1..v)+add(`if`(t=0, 0, b(n-1, sort([u+j-1, v+i-1])[], 0)), i=1..n-v), j=1..n-u)) end: a:= n-> b(n$3, 1): seq(a(n), n=0..21); -
Mathematica
nn = 20; a=Apply[Plus,Table[Normal[Series[y x^3/(1 - y x - y x^2), {x, 0, nn}]][[n]]/(n +2)!^2, {n, 1, nn - 2}]] /. y -> -1;Map[Select[#, # > 0 &] &, Range[0, nn]!^2 CoefficientList[Series[1/(1 - x - a), {x, 0, nn}], {x, y}]] // Flatten (* Geoffrey Critzer, Apr 27 2020 *)
Formula
a(n) <= A001044(n) with equality only for n < 3.