A116696 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.

1, 3, 6, 15, 29, 59, 99, 170, 262, 401, 570, 816, 1103, 1499, 1956, 2534, 3195, 4041, 4980, 6153, 7448, 8985, 10674, 12704, 14899, 17473, 20262, 23467, 26914, 30905, 35138, 39996, 45191, 50997

Offset

1,2

Comments

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.

Links

Table of n, a(n) for n=1..34.

Formula

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

Example

Examples: the two sets are indicated by X's and o's.
a(2) = 3:
XX oX oo
XX XX XX
--------------------
a(3) = 7:
XXX oXX ooX ooo ooX ooo
XXX XXX XXX XXX oXX oXX
XXX XXX XXX XXX XXX XXX
--------------------
a(4)= 15:
XXXX XXXX XXXX XXXX XXXX XXXX XXXX XXXX XXXX XXXX
XXXX XXXX XXXX XXXX XXXX XXXX XXXX XXXX XXXX XXXX
XXXX XXXX XXXX XXXX XXXX XXXo XXXo XXXo XXoo XXoo
XXXX XXXo XXoo Xooo oooo XXoo Xooo oooo Xooo oooo
----
XXXX XXXX XXXX XXXX XXXX
XXXo XXXX XXXX XXXo XXXo
XXoo Xooo oooo Xooo XXoo
Xooo oooo oooo oooo oooo

Crossrefs

Cf. A114043, A099957.

Sequence in context: A226736 A066708 A034464 * A000220 A244705 A319643

Adjacent sequences: A116693 A116694 A116695 * A116697 A116698 A116699

Keyword

nonn,more

Author

David Applegate, Feb 23 2006

Status

approved