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A343053 Table read by ascending antidiagonals: T(k, n) is the maximum vertex sum in a perimeter-magic k-gon of order n.

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%I A343053 #5 Apr 04 2021 01:00:15
%S A343053 15,24,24,40,42,33,54,65,56,42,77,93,90,74,51,96,126,126,115,88,60,
%T A343053 126,164,175,165,140,106,69,150,207,224,224,198,165,120,78,187,255,
%U A343053 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 A343053 Table read by ascending antidiagonals: T(k, n) is the maximum vertex sum in a perimeter-magic k-gon of order n.
%H A343053 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 A343053 T(k, n) = k*(1 + k*(2n - 3) - (n mod 2)*(1 - (k mod 2)))/2.
%F A343053 T(n, n) = A059270(n-1).
%e A343053 The table begins:
%e A343053 k\n|   3    4    5    6    7 ...
%e A343053 ---+------------------------
%e A343053 3  |  15   24   33   42   51 ...
%e A343053 4  |  24   42   56   74   88 ...
%e A343053 5  |  40   65   90  115  140 ...
%e A343053 6  |  54   93  126  165  198 ...
%e A343053 7  |  77  126  175  224  273 ...
%e A343053 ...
%t A343053 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 A343053 Cf. A005475 (n = 4), A022267 (n = 6), A059270, A179805 (k = 3), A343052 (minimum).
%K A343053 nonn,tabl
%O A343053 3,1
%A A343053 _Stefano Spezia_, Apr 03 2021