A341920 Number of simple strong triangulations of a fixed pentagon with n interior nodes.

1, 5, 20, 85, 385, 1836, 9120, 46805, 246675, 1328925, 7292688, 40652780, 229698220, 1313175880, 7585060680, 44212723797, 259808593975, 1537840085775, 9162371040900, 54913015836525, 330888232445505, 2003659057873200, 12187811305300800, 74444226847892460, 456458831442283860

Offset

1,2

Links

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

Formula

From Peter Bala, Feb 06 2022: (Start)

Conjectures:

a(n) = 5*(5*n-3)*binomial(3*n,n)/((n+1)*(2*n+1)*(2*n+3)).

a(n+1) = 3*(3*n+1)*(3*n+2)*(5*n+2)/(2*(n+2)*(2*n+5)*(5*n-3))*a(n). (End)

Prog

(PARI) R(25, 2) \\ R defined in A210664.

Crossrefs

Row m = 2 of A210664.

Cf. A000256, A341917.

Sequence in context: A126987 A152185 A152187 * A045499 A358518 A145932

Adjacent sequences: A341917 A341918 A341919 * A341921 A341922 A341923

Keyword

nonn

Author

Andrew Howroyd, Feb 24 2021

Status

approved