A387202 a(n) is the number of dissections of a (4*n+2)-gon into hexagons using strictly disjoint diagonals.
1, 5, 21, 87, 363, 1534, 6570, 28492, 124944, 553301, 2471373, 11122275, 50389695, 229643895, 1052093655, 4842863465, 22386911925, 103885321615, 483759492255, 2259888333445, 10587902977185, 49738841822400, 234235771140876, 1105609645231322, 5229610939919718
Offset: 1
Links
- Muhammed Sefa Saydam, Table of n, a(n) for n = 1..100
Programs
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PARI
seq(n)={my(g=(1 - 3*x - sqrt(1 - 6*x + 5*x^2 + O(x*x^n)))/(2*x)); Vec((1 + 4*g + 3*g^2)*x + g^2)} \\ Andrew Howroyd, Aug 21 2025
Formula
G.f.: x*(1 + 4*B(x) + 3*B(x)^2) + B(x)^2, where 1 + B(x) is the g.f. of A002212. - Andrew Howroyd, Aug 21 2025
D-finite with recurrence -(n+2)*(2*n-3)*a(n) +3*(2*n+1)*(2*n-3)*a(n-1) -5*(2*n+1)*(n-3)*a(n-2)=0. - R. J. Mathar, Aug 28 2025