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

0,2

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).

Links

Table of n, a(n) for n=0..21.

Peter J. Taylor, Python program to generate terms

Example

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-

Crossrefs

Cf. A114043.

Sequence in context: A364399 A365568 A360939 * A365585 A012056 A062971

Adjacent sequences: A114528 A114529 A114530 * A114532 A114533 A114534

Keyword

nonn

Author

David Applegate, Feb 24 2006

Extensions

More terms from Peter J. Taylor, Feb 28 2019

Status

approved