This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A387224 #24 Sep 03 2025 18:27:35 %S A387224 0,1,1,4,8,17,37,81,177,389,859,1905,4241,9477,21251,47806,107864, %T A387224 244045,553575,1258687,2868285,6549757,14985361,34347444,78860152, %U A387224 181347591,417653187,963234195,2224464087,5143567237,11907471643,27597112946,64028244032,148703128913,345690623119 %N A387224 Number of dissections of a convex n-gon by strictly disjoint diagonals so as to create no triangles. %C A387224 Strictly disjoint diagonals means that the diagonals are non-crossing and may not share endpoints. %H A387224 Muhammed Sefa Saydam, <a href="/A387224/b387224.txt">Table of n, a(n) for n = 3..104</a> %F A387224 a(n) = A004149(n) - A004149(n-2) - 2*A004149(n-3) for n >= 5. %F A387224 G.f.: (1 - x^2 - 2*x^3)*B(x) - 1 - x + 2*x^3 + 2*x^4, where B(x) is the g.f. of A004149. - _Andrew Howroyd_, Aug 28 2025 %e A387224 n=4 n=5 n=6 %e A387224 (1) (2) (1) (1) (2) (1) (2) (1) (2) %e A387224 (5) (2) (6) \ (3) (6)-----(3) (6) / (3) %e A387224 (4) (3) (4) (3) (5) (4) (5) (4) (5) (4) %e A387224 Diagonal cannot be drawn Diagonal cannot be drawn %e A387224 Number of cases = 1 Number of cases = 1 Number of cases = 3 %o A387224 (PARI) seq(n) = my(g=2/(1 - x + x^2 + x^3 + sqrt((1-x^4)*(1-2*x-x^2) + O(x*x^n)))); Vec((1 - x^2 - 2*x^3)*g - 1 - x + 2*x^3 + 2*x^4, -n+2) \\ _Andrew Howroyd_, Aug 28 2025 %Y A387224 Cf. A004149, A093128. %K A387224 nonn,new %O A387224 3,4 %A A387224 _Muhammed Sefa Saydam_, Aug 22 2025