OFFSET
0,3
LINKS
Matteo Cervetti and Luca Ferrari, Pattern avoidance in the matching pattern poset, arXiv:2009.01024 [math.CO], 2020.
Matteo Cervetti and Luca Ferrari, Enumeration of Some Classes of Pattern Avoiding Matchings, with a Glimpse into the Matching Pattern Poset, Annals of Combinatorics (2022).
FORMULA
G.f.: (1-sqrt(1-4*x))/(2*x) + 1/(1-2*x) - 1/(x-1)^2. - Alois P. Heinz, Dec 01 2020
D-finite with recurrence -(n+1)*(385*n-1369)*a(n) +2*(1651*n^2 -6079*n +1369)*a(n-1) +(-9639*n^2 +44846*n -43507)*a(n-2) +2*(5789*n^2 -31763*n +43223)*a(n-3) -4*(607*n -1524)*(2*n-7)*a(n-4)=0. - R. J. Mathar, Dec 11 2020
MAPLE
a:= proc(n) option remember; `if`(n<4, ceil(3^(n-1)),
((2*(1651*n^2-6079*n+1369))*a(n-1)-(9639*n^2-44846*n+43507)*
a(n-2)+(2*(5789*n^2-31763*n+43223))*a(n-3)-(4*(607*n-1524))*
(2*n-7)*a(n-4))/((n+1)*(385*n-1369)))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Dec 05 2020
MATHEMATICA
Table[CatalanNumber[n]+2^n-n-1, {n, 0, 30}] (* Harvey P. Dale, Nov 24 2022 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 30 2020
STATUS
approved