A363582 Number of admissible mesa sets among Stirling permutations of order n.

1, 2, 3, 6, 12, 22, 44, 88, 169, 338, 676, 1322, 2644, 5288, 10433, 20866, 41732, 82736, 165472, 330944, 658012, 1316024, 2632048, 5242778, 10485556, 20971112, 41822049, 83644098, 167288196, 333885702, 667771404, 1335542808, 2667053601, 5334107202, 10668214404

Offset

1,2

References

Nicolle González, Pamela E. Harris, Gordon Rojas Kirby, Mariana Smit Vega Garcia, and Bridget Eileen Tenner, "Mesas of Stirling permutations," preprint.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..3323

Formula

Let n = 3*k+r, where r is in {0,1,2}, and let C_(x,y) be the rational Catalan numbers (A328901/A328902). Then a(n) = 2^(n-1) - Sum_{i=0..k-1} 2^(3*i+r)*C_(2*(k-i)-1,k-i).

Example

For n = 4, the a(4) = 6 admissible pinnacle sets for Stirling permutations of order 4 are {}, {2}, {3}, {4}, {2,4}, and {3,4}.

Maple

a:= proc(n) option remember; `if`(n<4, n, (2*n*(2*n-3)*
      a(n-1)+27*(n-4)*(n-2)*(a(n-3)/2-a(n-4)))/(n*(2*n-3)))
    end:
seq(a(n), n=1..45);  # Alois P. Heinz, Jun 13 2023

Crossrefs

Cf. A289871, A359066, A359067, A328901, A328902.

Sequence in context: A060985 A371793 A355850 * A068012 A261930 A019138

Adjacent sequences: A363579 A363580 A363581 * A363583 A363584 A363585

Keyword

nonn

Author

Bridget Tenner, Jun 10 2023

Extensions

More terms from Alois P. Heinz, Jun 13 2023

Status

approved