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A342758 Array read by ascending antidiagonals: T(k, n) is the maximum value of the magic constant in a perimeter-magic k-gon of order n.

%I A342758 #5 Mar 23 2021 16:18:40
%S A342758 12,15,23,19,30,37,22,37,48,54,26,44,60,71,74,29,51,71,88,97,97,33,58,
%T A342758 83,105,121,128,123,36,65,94,122,144,159,162,152,40,72,106,139,168,
%U A342758 190,202,201,184,43,79,117,156,191,221,241,250,243,219,47,86,129,173,215,252,281,299,303,290,257
%N A342758 Array read by ascending antidiagonals: T(k, n) is the maximum value of the magic constant in a perimeter-magic k-gon of order n.
%H A342758 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 11 and 13).
%F A342758 G.f.: (- x^2*(2*y^2 + y - 1) - x*(y^2 + 2*y - 1) + (y - 1)*y^2)/((x - 1)^2*(x + 1)*(y - 1)^3*(y + 1)).
%F A342758 T(k, n) = (n^2/2 - 1)*k + n/2 if n is even or both n and k are odd.
%F A342758 T(k, n) = (n^2/2 - 1)*k + (n - 1)/2 if n is odd and k is even.
%F A342758 T(k, n) = (n + k*(n^2 - 2) + ((k mod 2) - 1)*(n mod 2))/2.
%e A342758 The array begins:
%e A342758 k\n|  3   4   5    6    7 ...
%e A342758 ---+---------------------
%e A342758 3  | 12  23  37   54   74 ...
%e A342758 4  | 15  30  48   71   97 ...
%e A342758 5  | 19  37  60   88  121 ...
%e A342758 6  | 22  44  71  105  144 ...
%e A342758 7  | 26  51  83  122  168 ...
%e A342758 ...
%t A342758 T[k_,n_]:= (n+k(n^2-2)+(Mod[k,2]-1)Mod[n,2])/2; Table[T[k+3-n,n],{k,3,13},{n,3,k}]//Flatten
%Y A342758 Cf. A017005 (n = 4), A135503 (diagonal), A341740 (k = 3), A342719, A342757 (minimum).
%K A342758 nonn,tabl
%O A342758 3,1
%A A342758 _Stefano Spezia_, Mar 21 2021