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A114531 Number of intersections of a convex set with the n X n grid. 3
1, 2, 16, 214, 2856, 33367, 349895, 3302046, 28597720, 229893484, 1730841042, 12296287989, 82945782429, 533994100001, 3295058878301, 19560004053448, 112049953456910, 621112646095769, 3339451666010949, 17451533356424837, 88807504851447189, 440798078343276894 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
David Applegate, Feb 24 2006
EXTENSIONS
More terms from Peter J. Taylor, Feb 28 2019
STATUS
approved

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Last modified July 15 14:40 EDT 2024. Contains 374332 sequences. (Running on oeis4.)