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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.
1
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
1,4
COMMENTS
This sequence is the sum of the sequences A342720 and A342722 which deal with concave and convex quadrilaterals respectively.
FORMULA
a(n) = A342720(n) + A342722(n).
EXAMPLE
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
KEYWORD
nonn
AUTHOR
Herbert Kociemba, May 22 2021
STATUS
approved