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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: 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

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