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

3,4

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

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).

Crossrefs

Cf. A093128, A159284, A387224.

Sequence in context: A384869 A259571 A291212 * A125570 A268111 A369920

Adjacent sequences: A387264 A387265 A387266 * A387268 A387269 A387270

Keyword

nonn

Author

Muhammed Sefa Saydam, Aug 24 2025

Status

approved