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%I #5 Feb 01 2023 08:00:33
%S 1,3,6,15,29,59,99,170,262,401,570,816,1103,1499,1956,2534,3195,4041,
%T 4980,6153,7448,8985,10674,12704,14899,17473,20262,23467,26914,30905,
%U 35138,39996,45191,50997
%N Take an n X n square grid of points in the plane; a(n) = number of non-isomorphic ways to divide the points into two sets using a straight line.
%C The line may not pass through any point. This is the "unlabeled" version - rotations and reflections are taken into account. See A114043 for the "labeled" version.
%F if n is even, then a(n) = (A114043(n) + 6n + 3 + 2 A099957(n/2))/8 if n is odd, then a(n) = (A114043(n) + 6n + 1)/8
%e Examples: the two sets are indicated by X's and o's.
%e a(2) = 3:
%e XX oX oo
%e XX XX XX
%e --------------------
%e a(3) = 7:
%e XXX oXX ooX ooo ooX ooo
%e XXX XXX XXX XXX oXX oXX
%e XXX XXX XXX XXX XXX XXX
%e --------------------
%e a(4)= 15:
%e XXXX XXXX XXXX XXXX XXXX XXXX XXXX XXXX XXXX XXXX
%e XXXX XXXX XXXX XXXX XXXX XXXX XXXX XXXX XXXX XXXX
%e XXXX XXXX XXXX XXXX XXXX XXXo XXXo XXXo XXoo XXoo
%e XXXX XXXo XXoo Xooo oooo XXoo Xooo oooo Xooo oooo
%e ----
%e XXXX XXXX XXXX XXXX XXXX
%e XXXo XXXX XXXX XXXo XXXo
%e XXoo Xooo oooo Xooo XXoo
%e Xooo oooo oooo oooo oooo
%Y Cf. A114043, A099957.
%K nonn,more
%O 1,2
%A _David Applegate_, Feb 23 2006
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