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

Author

Bridget Tenner, Jun 10 2023

Keywords

• nonn

Examples

			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}.
		

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

Crossrefs

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

Programs

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

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).

Extensions

More terms from Alois P. Heinz, Jun 13 2023