A045744 Number of noncrossing connected graphs on n nodes on a circle having no four-sided faces.

1, 4, 22, 141, 988, 7337, 56749, 452332, 3689697, 30652931, 258465558, 2206330790, 19029531220, 165582392070, 1451789520435, 12813638048184, 113755675163767, 1015119850103821, 9100463691522759, 81923222827031025

Offset: 2

Author

Emeric Deutsch

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..200

Crossrefs

Column k=0 of A094046.

Cf. A045743.

Programs

PARI

a(n) = if(n>1, sum(i=0, floor((n-2)/3), binomial(n-2+i, i)*binomial(4*n-4-i, n-2-3*i))/(n-1)); \\ Andrew Howroyd, Nov 12 2017

Formula

a(n) = Sum_{i=0..floor((n-2)/3)} binomial(n-2+i, i)*binomial(4*n-4-i, n-2-3*i)/(n-1).