A114531 Number of intersections of a convex set with the n X n grid.

1, 2, 16, 214, 2856, 33367, 349895, 3302046, 28597720, 229893484, 1730841042, 12296287989, 82945782429, 533994100001, 3295058878301, 19560004053448, 112049953456910, 621112646095769, 3339451666010949, 17451533356424837, 88807504851447189, 440798078343276894

Offset: 0

Author

David Applegate, Feb 24 2006

Keywords

• nonn

Comments

This is a generalization of A114043, which can be viewed as the number of intersections of a halfspace with the n X n grid (divided by 2).

Examples

			a(3) = 214 (X's indicate points in intersection):
... X.. .X. ... XX. X.. X.. X.. XXX XX. XX. XX. X.. X.. .X. .X.
... ... ... .X. ... .X. ..X ... ... X.. .X. ..X .XX .X. .X. XX.
... ... ... ... ... ... ... .X. ... ... ... ... ... ..X .X. ...
-1- -4- -4- -1- -8- -4- -8- -8- -4- -4- -8- -8- -8- -2- -2- -4-
XXX XXX XX. XX. XX. XX. .X. X.. XXX XXX XX. XX. XX. XX. .X. XX.
X.. .X. XX. .X. .XX .X. XXX .XX XX. .X. .XX .XX XXX XX. XXX .X.
... ... ... .X. ... ..X ... .X. ... .X. ..X .X. ... ..X .X. .XX
-8- -4- -4- -8- -8- -8- -4- -4- -8- -4- -4- -8- -8- -4- -1- -4-
XXX XXX XXX XX. XX. XXX XXX XX. XXX XXX
XXX XX. XX. XXX XXX XXX XXX XXX XXX XXX
... X.. .X. .X. ..X X.. .X. .XX XX. XXX
-4- -4- -8- -4- -8- -8- -4- -2- -4- -1-
		

Links

• Peter J. Taylor, Python program to generate terms

Crossrefs

Cf. A114043.

Extensions

More terms from Peter J. Taylor, Feb 28 2019