A386538 a(n) is the maximum possible area of a polygon within a circle of radius n, where both the center and the vertices lie on points of a unit square grid.
0, 2, 8, 24, 42, 74, 104, 138, 186, 240, 304, 362, 424, 512, 594, 690, 776, 880, 986, 1104, 1232, 1346, 1490, 1624, 1762, 1930, 2088, 2256, 2418, 2594, 2784, 2962, 3170, 3368, 3584, 3810, 4008, 4248, 4466, 4730, 4976, 5210, 5474, 5736, 6024, 6306, 6570, 6864, 7154
Offset: 0
Keywords
Examples
See linked illustration of the term a(4) = 42.
Links
- Felix Huber, Table of n, a(n) for n = 0..10000
- Felix Huber, Illustration of a(4) = 42
- Eric Weisstein's World of Mathematics, Pick's Theorem
Programs
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Maple
A386538:=proc(n) local x,y,p,s; p:=4*n; s:={}; for x to n do y:=floor(sqrt(n^2-x^2)); p:=p+4*y; s:=s union {y} od; return p-2*nops(s) end proc; seq(A386538(n),n=0..48);
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Mathematica
a[n_] := Module[{p=4n},s = {}; Do[ y = Floor[Sqrt[n^2 - x^2]];p = p + 4*y;s = Union[s, {y}],{x,n} ];p - 2*Length[s]];Array[a,49,0] (* James C. McMahon, Aug 19 2025 *)
Comments