A116696 - OEIS

%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