

A340489


Number of distinct integersided 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
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OFFSET

0,8


LINKS

Table of n, a(n) for n=0..73.


FORMULA

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((nk)/3)} Sum_{i=j..floor((njk)/2)} (2  [k = j])*(1 + sign(ceiling((k+j)/sqrt((nijk)^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



