A344528 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) and integer diagonals e,f.

0, 0, 0, 2, 2, 1, 5, 7, 8, 5, 7, 13, 14, 11, 16, 31, 20, 14, 19, 33, 26, 26, 24, 67, 43, 39, 53, 62, 36, 53, 40, 94, 72, 48, 73, 77, 64, 60, 94, 122, 58, 75, 68, 106, 109, 81, 62, 195, 114, 113, 140, 151, 87, 129, 143, 235, 154, 97, 92, 266

Offset: 1

Author

Herbert Kociemba, May 22 2021

Keywords

• nonn

Comments

This sequence is the sum of the sequences A342720 and A342722 which deal with concave and convex quadrilaterals respectively.

Examples

			a(6)=1 because the only integer quadrilateral with longest edge length 6 is a trapezoid with sides a=6, b=5, c=4, d=5 and diagonals e=f=7.
		

Crossrefs

Cf. A342720, A342721, A342722, A342723, A344529.

Formula

a(n) = A342720(n) + A342722(n).