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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

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: A188600 A206930 A206865 * A012056 A062971 A267782

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

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Last modified March 2 19:18 EST 2021. Contains 341756 sequences. (Running on oeis4.)