A344529 a(n) is the number of integer quadrilaterals (up to congruence) with integer side lengths a,b,c,d with n = Max(a,b,c,d), integer diagonals e,f and integer area.

0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 2, 1, 1, 4, 1, 4, 0, 0, 6, 3, 0, 0, 7, 8, 3, 0, 5, 3, 8, 0, 1, 0, 5, 5, 3, 10, 0, 10, 11, 5, 5, 0, 3, 5, 0, 0, 11, 0, 11, 18, 15, 5, 0, 6, 10, 0, 6, 0, 26, 4, 0, 11, 1, 32, 3, 0, 10, 2, 10, 0, 10, 12, 17, 34

Offset: 1

Author

Herbert Kociemba, May 22 2021

Keywords

• nonn

Comments

This sequence is the sum of the sequences A342721 and A342723 which deal with concave and convex quadrilaterals respectively.

Examples

			a(4)=1 because the smallest possible quadrilateral is a rectangle with a=c=4, b=d=3, e=f=5 and area 12.
		

Crossrefs

Cf. A342720, A342721, A342722, A342723, A344528.

Formula

a(n) = A342721(n) + A342723(n).