A387267 Number of dissections of a convex n-gon into quadrilaterals and pentagons by strictly disjoint diagonals.

0, 1, 1, 3, 7, 8, 19, 31, 47, 87, 135, 219, 371, 579, 947, 1535, 2423, 3919, 6239, 9891, 15803, 24987, 39563, 62663, 98751, 155815, 245431, 385771, 606467, 951795, 1492323, 2338703, 3660551, 5725951, 8950543, 13978931, 21820235, 34037067, 53059643, 82670167

Offset: 3

Author

Muhammed Sefa Saydam, Aug 24 2025

Keywords

• nonn
• new

Comments

Strictly disjoint diagonals means that the diagonals are non-crossing and may not share endpoints.

Links

• Muhammed Sefa Saydam, Table of n, a(n) for n = 3..100

Crossrefs

Cf. A093128, A159284, A387224.

Formula

a(n) = T(n-3) + Sum_{i=1..n-8} T(i)*( T(n-i-4) + T(n-i-7) ) + Sum_{i=n-7..n-5} T(i)*( 1 + T(n-i-4) ) for n >= 9 and T(n) = A159284(n).