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 A340489 Number of distinct integer-sided convex quadrilaterals with perimeter n whose largest two sides form a right angle. 0
 0, 0, 0, 0, 1, 0, 0, 2, 1, 1, 0, 2, 1, 1, 4, 2, 3, 1, 4, 5, 3, 7, 4, 6, 8, 7, 10, 6, 12, 7, 10, 16, 12, 16, 10, 18, 18, 16, 25, 18, 24, 24, 26, 30, 24, 36, 26, 34, 40, 36, 44, 34, 49, 45, 46, 58, 49, 60, 46, 64, 67, 61, 78, 64, 79, 83, 82, 91, 79, 101, 82, 99, 112, 103 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 LINKS FORMULA a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} (2 - [k = j])*(-1 + sign(ceiling((k+j)/sqrt((n-i-j-k)^2 + i^2)))), where [ ] is the Iverson bracket. EXAMPLE The notation [q,r,s,t] below shows the order in which the sides are joined (counterclockwise) starting with the largest side q, the second largest side r, and then each of the possible orders in which s and t can occur. a(4) = 1; [1,1,1,1] a square. a(5) = 0; ( not [2,1,1,1] since sqrt(2^2+1^2) = sqrt(5) > 1+1 = 2. ) a(7) = 2; [2,2,2,1], [2,2,1,2]. a(14) = 4; [5,3,3,3], [4,4,4,2], [4,4,3,3], and [4,4,2,4]. MATHEMATICA Table[Sum[Sum[Sum[(2 - KroneckerDelta[k, j]) Sign[Ceiling[(j + k)/Sqrt[(n - i - j - k)^2 + i^2]] - 1], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 80}] CROSSREFS Sequence in context: A125072 A162642 A139146 * A277487 A144032 A137686 Adjacent sequences:  A340486 A340487 A340488 * A340490 A340491 A340492 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Jan 09 2021 STATUS approved

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Last modified May 9 19:47 EDT 2021. Contains 343746 sequences. (Running on oeis4.)