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

1,2

Links

Muhammed Sefa Saydam, Table of n, a(n) for n = 1..100

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

Prog

(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

Crossrefs

Cf. A002212, A093128.

Sequence in context: A012814 A039919 A322875 * A292494 A010925 A019992

Adjacent sequences: A387199 A387200 A387201 * A387203 A387204 A387205

Keyword

nonn

Author

Muhammed Sefa Saydam, Aug 21 2025

Status

approved