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A331755
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Number of vertices in a regular drawing of the complete bipartite graph K_{n,n}.
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28
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2, 5, 13, 35, 75, 159, 275, 477, 755, 1163, 1659, 2373, 3243, 4429, 5799, 7489, 9467, 11981, 14791, 18275, 22215, 26815, 31847, 37861, 44499, 52213, 60543, 70011, 80347, 92263, 105003, 119557, 135327, 152773, 171275, 191721, 213547, 237953
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OFFSET
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1,1
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LINKS
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FORMULA
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MAPLE
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V106i := proc(n) local ans, a, b; ans:=0;
for a from 1 to n-1 do for b from 1 to n-1 do
if igcd(a, b)=1 then ans:=ans + (n-a)*(n-b); fi; od: od: ans; end; # A115004
V106ii := proc(n) local ans, a, b; ans:=0;
for a from 1 to floor(n/2) do for b from 1 to floor(n/2) do
if igcd(a, b)=1 then ans:=ans + (n-2*a)*(n-2*b); fi; od: od: ans; end; # A331761
A331755 := n -> 2*(n+1) + V106i(n+1) - V106ii(n+1);
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MATHEMATICA
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a[n_]:=Module[{x, y, s1=0, s2=0}, For[x=1, x<=n-1, x++, For[y=1, y<=n-1, y++, If[GCD[x, y]==1, s1+=(n-x)*(n-y); If[2*x<=n-1&&2*y<=n-1, s2+=(n-2*x)*(n-2*y)]]]]; s1-s2]; Table[a[n]+ 2 n, {n, 1, 40}] (* Vincenzo Librandi, Feb 04 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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