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A281700 Number of examples for Simpson's paradox with data items in {0,1,...,n}. 1
0, 0, 0, 30, 456, 3396, 14538, 52840, 150116, 380336, 860924, 1839406, 3551856, 6684280, 11834214, 20108168, 33051136, 53176968 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Number of octuples (a,b,c,d,w,x,y,z) in {0,1,...,n}^8 with a*d > b*c, w*z > x*y and (a+w)*(d+z) < (b+x)*(c+y).

All terms are even. If (a,b,c,d,w,x,y,z) is an example then (w,x,y,z,a,b,c,d) is a different example.

LINKS

Table of n, a(n) for n=0..17.

Wikipedia, Simpson's paradox

EXAMPLE

a(3) = 30: (1,0,2,1,1,3,0,1), (1,0,3,1,1,2,0,1), (1,0,3,1,1,3,0,1), (1,0,3,1,1,3,0,2), (1,0,3,1,1,3,0,3), (1,0,3,1,2,3,0,1), (1,0,3,1,2,3,1,2), (1,0,3,1,3,3,0,1), (1,0,3,2,1,3,0,1), (1,0,3,2,1,3,0,2), (1,0,3,3,1,3,0,1), (1,2,0,1,1,0,3,1), (1,3,0,1,1,0,2,1), (1,3,0,1,1,0,3,1), (1,3,0,1,1,0,3,2), (1,3,0,1,1,0,3,3), (1,3,0,1,2,0,3,1), (1,3,0,1,2,1,3,2), (1,3,0,1,3,0,3,1), (1,3,0,2,1,0,3,1), (1,3,0,2,1,0,3,2), (1,3,0,3,1,0,3,1), (2,0,3,1,1,3,0,1), (2,0,3,1,2,3,0,1), (2,1,3,2,1,3,0,1), (2,3,0,1,1,0,3,1), (2,3,0,1,2,0,3,1), (2,3,1,2,1,0,3,1), (3,0,3,1,1,3,0,1), (3,3,0,1,1,0,3,1).

MAPLE

a:= n-> (g-> add(add((h-> `if`(h[1]*h[4] < h[2]*h[3], 2, 0))(

         g[i]+g[j]), j=1..i-1), i=2..nops(g)))(select(f->

         f[1]*f[4] > f[2]*f[3], [seq(seq(seq(seq([w, x, y, z],

         w=0..n), x=0..n), y=0..n), z=0..n)])):

seq(a(n), n=0..8);

CROSSREFS

Cf. A281614.

Sequence in context: A006421 A035710 A042746 * A024524 A081736 A161573

Adjacent sequences:  A281697 A281698 A281699 * A281701 A281702 A281703

KEYWORD

nonn,more

AUTHOR

Alois P. Heinz, Jan 27 2017

STATUS

approved

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Last modified March 20 09:35 EDT 2019. Contains 321345 sequences. (Running on oeis4.)