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Number of different convex quadrilaterals that can be formed from n congruent isosceles right triangles. Reflections are not counted as different.
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%I #18 Sep 16 2017 19:19:49

%S 0,2,2,5,2,5,3,9,2,5,2,11,2,6,4,13,3,7,2,11,4,5,3,19,2,5,4,12,2,10,3,

%T 17,4,6,4,16,2,5,4,19,3,10,2,11,6,6,3,27,3,7,4,11,2,10,4,20,4,5,2,22,

%U 2,6,7,21,4,10,2,12,4,10,3,28,3,5,6,11,4,10

%N Number of different convex quadrilaterals that can be formed from n congruent isosceles right triangles. Reflections are not counted as different.

%C Illustrated with other convex polyabolos in A245676.

%H Andrew Howroyd, <a href="/A292146/b292146.txt">Table of n, a(n) for n = 1..1000</a>

%H Andrew Howroyd, <a href="/A292146/a292146.txt">Convex Quadrilaterals formed from Polyabolos</a>

%e For n=2, there is a square and a parallelogram.

%o (PARI) \\ here b is A100073

%o b(n) = if(n%2, floor(numdiv(n)/2), if(n%4, 0, floor(numdiv(n/4)/2)));

%o d(n) = my(t); sum(k=1, floor(sqrt((n-1)/2)), issquare(n+2*k^2,&t) && t>2*k);

%o a(n) = 2*b(n) + d(n) + if(n%2, 0, 2*numdiv(n/2) + b(n/2)) + if(n%4, 0, ceil(numdiv(n/4)/2)); \\ _Andrew Howroyd_, Sep 16 2017

%Y Strictly less than A245676.

%K nonn

%O 1,2

%A _Douglas J. Durian_, Sep 09 2017

%E Terms a(33) and beyond from _Andrew Howroyd_, Sep 16 2017