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URL: https://oeis.org/A380980

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A380980
Place 2n distinct positive integers on an n-gon, n on the vertices and n on the sides such that the sums of the three values on all sides are equal. a(n) is the minimal sum of all the integers used.
0
21, 38, 55, 81, 105, 140
OFFSET
3,1
EXAMPLE
For n=7 the first 14 positive integers suffice. Their permutation is 1,11,7,8,4,9,6,10,3,14,2,12,5,13 and the sum on each side of the heptagon is 19.
MATHEMATICA
mod[n_]:=Append[n, First[n]];
plus[n_]:=Table[mod[n][[i]]+mod[n][[i+1]], {i, 1, Length[mod[n]]-1}];
goodPermutations[n_]:=Select[Permutations[n], Length[plus[#]]==Length[Union[plus[#]]]&];
min[n_]:=Min[Max/@plus/@goodPermutations[Range[n]]];
bestPermutation[n_]:=Select[goodPermutations[Range[n]], Max[plus[#]]==min[n]&, 1];
plusBP[n_]:=plus/@bestPermutation[n]; max[n_]:=Max[Max/@plusBP[n]];
unit[n_]:=max[n]+n+1; sum[n_]:=n*unit[n]-Total@@plusBP[n]+n*(n+1)/2; sum/@Range[3, 8]
CROSSREFS
Cf. A380853.
Sequence in context: A050782 A061906 A385333 * A139768 A307278 A176071
KEYWORD
nonn,more
AUTHOR
Ivan N. Ianakiev, Feb 10 2025
STATUS
approved