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%I #5 Apr 04 2021 01:00:15
%S 15,24,24,40,42,33,54,65,56,42,77,93,90,74,51,96,126,126,115,88,60,
%T 126,164,175,165,140,106,69,150,207,224,224,198,165,120,78,187,255,
%U 288,292,273,237,190,138,87,216,308,350,369,352,322,270,215,152,96,260,366,429,455,450,420,371,309,240,170,105
%N Table read by ascending antidiagonals: T(k, n) is the maximum vertex sum in a perimeter-magic k-gon of order n.
%H Terrel Trotter, <a href="https://web.archive.org/web/20070106085340/http://www.trottermath.net/simpleops/pmp.html">Perimeter-Magic Polygons</a>, Journal of Recreational Mathematics Vol. 7, No. 1, 1974, pp. 14-20 (see equations 6 and 8).
%F T(k, n) = k*(1 + k*(2n - 3) - (n mod 2)*(1 - (k mod 2)))/2.
%F T(n, n) = A059270(n-1).
%e The table begins:
%e k\n| 3 4 5 6 7 ...
%e ---+------------------------
%e 3 | 15 24 33 42 51 ...
%e 4 | 24 42 56 74 88 ...
%e 5 | 40 65 90 115 140 ...
%e 6 | 54 93 126 165 198 ...
%e 7 | 77 126 175 224 273 ...
%e ...
%t T[k_,n_]:=k(1+k(2n-3)-Mod[n,2](1-Mod[k,2]))/2; Table[T[k+3-n,n],{k,3,14},{n,3,k}]//Flatten
%Y Cf. A005475 (n = 4), A022267 (n = 6), A059270, A179805 (k = 3), A343052 (minimum).
%K nonn,tabl
%O 3,1
%A _Stefano Spezia_, Apr 03 2021