Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Feb 09 2024 14:22:44
%S 1,1,4,6,26,45,204,380,1771,3450,16380,32886,158224,324632,1577532,
%T 3290040,16112057,34034715,167710664,357919100,1772645420,3815041230,
%U 18974357220,41124015036,205263418941,447534498320,2240623268512,4910258796240,24648785802336,54257308779600
%N Number of achiral dissections of a polygon into n hexagons by nonintersecting diagonals rooted at a cell.
%H Andrew Howroyd, <a href="/A370061/b370061.txt">Table of n, a(n) for n = 1..1000</a>
%F a(2*n) = 6*binomial(5*n+1, n-1)/(5*n+1); a(2*n+1) = 4*binomial(5*n+4, n)/(5*n+4).
%o (PARI) a(n)=my(m=n\2); if(n%2==0, 6*binomial(5*m+1, m-1)/(5*m+1), 4*binomial(5*m+4, m)/(5*m+4))
%Y Column k=6 of A370060.
%K nonn
%O 1,3
%A _Andrew Howroyd_, Feb 08 2024