A363582 - OEIS

%I #21 Jun 14 2023 12:12:07

%S 1,2,3,6,12,22,44,88,169,338,676,1322,2644,5288,10433,20866,41732,

%T 82736,165472,330944,658012,1316024,2632048,5242778,10485556,20971112,

%U 41822049,83644098,167288196,333885702,667771404,1335542808,2667053601,5334107202,10668214404

%N Number of admissible mesa sets among Stirling permutations of order n.

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

%H Alois P. Heinz, <a href="/A363582/b363582.txt">Table of n, a(n) for n = 1..3323</a>

%F 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).

%e 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}.

%p a:= proc(n) option remember; `if`(n<4, n, (2*n*(2*n-3)*

%p       a(n-1)+27*(n-4)*(n-2)*(a(n-3)/2-a(n-4)))/(n*(2*n-3)))

%p     end:

%p seq(a(n), n=1..45);  # _Alois P. Heinz_, Jun 13 2023

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

%K nonn

%O 1,2

%A _Bridget Tenner_, Jun 10 2023

%E More terms from _Alois P. Heinz_, Jun 13 2023