A341917 Number of strong triangulations of a fixed pentagon with n interior nodes.

1, 10, 80, 610, 4625, 35322, 272800, 2132310, 16861455, 134781350, 1088074064, 8863227100, 72789560025, 602232150810, 5016320750400, 42041168169712, 354326295908580, 3001705818071400, 25549873091193600, 218426240780417250, 1874878554813727815, 16153461053030605590

Offset

1,2

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Formula

a(n) = 60*(13*n+9)*(4*n+5)!/((3*n+9)!*(n-1)!).

a(n) ~ 65 * 2^(8*n+25/2) / (3^(3*n+17/2) * n^(5/2) * sqrt(Pi)). - Amiram Eldar, Jan 08 2026

Mathematica

a[n_] := 60*(13*n + 9)*(4*n + 5)!/((3*n + 9)!*(n - 1)!); Array[a, 22] (* Amiram Eldar, Jan 08 2026 *)

Prog

(PARI) a(n)={60*(13*n+9)*(4*n+5)!/((3*n+9)!*(n-1)!)}

Crossrefs

Column k=2 of A341856.

Cf. A341853.

Sequence in context: A257286 A125373 A093145 * A369474 A037509 A037692

Adjacent sequences: A341914 A341915 A341916 * A341918 A341919 A341920

Keyword

nonn

Author

Andrew Howroyd, Feb 23 2021

Status

approved