A370061 Number of achiral dissections of a polygon into n hexagons by nonintersecting diagonals rooted at a cell.

1, 1, 4, 6, 26, 45, 204, 380, 1771, 3450, 16380, 32886, 158224, 324632, 1577532, 3290040, 16112057, 34034715, 167710664, 357919100, 1772645420, 3815041230, 18974357220, 41124015036, 205263418941, 447534498320, 2240623268512, 4910258796240, 24648785802336, 54257308779600

Offset: 1

Author

Andrew Howroyd, Feb 08 2024

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

Column k=6 of A370060.

Programs

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))

Formula

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).