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A342757 Array read by ascending antidiagonals: T(k, n) is the minimum value of the magic constant in a perimeter-magic k-gon of order n.

%I A342757 #10 Dec 23 2024 03:17:40
%S A342757 9,12,17,14,22,28,17,27,37,42,19,32,45,55,59,22,37,54,68,78,79,24,42,
%T A342757 62,81,96,104,102,27,47,71,94,115,129,135,128,29,52,79,107,133,154,
%U A342757 167,169,157,32,57,88,120,152,179,200,210,208,189,34,62,96,133,170,204,232,251,258,250,224
%N A342757 Array read by ascending antidiagonals: T(k, n) is the minimum value of the magic constant in a perimeter-magic k-gon of order n.
%H A342757 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 10 and 12).
%F A342757 G.f.: (x^2*(-3*y^3 + 2*y - 1) - x*(2*y^3 + y^2 - 2*y + 1) + (y - 1)*y)/((x - 1)^2*(x + 1)*(y - 1)^3*(y + 1)).
%F A342757 T(k, n) = (n^2/2 - n + 1)*k + n/2 if n is even or both n and k are odd.
%F A342757 T(k, n) = (n^2/2 - n + 1)*k + (n + 1)/2 if n is odd and k is even.
%F A342757 T(k, n) = ((1 - (k mod 2))*(n mod 2) + k*(n^2 - 2*n + 2) + n)/2.
%e A342757 The array begins:
%e A342757 k\n|  3   4   5   6    7 ...
%e A342757 ---+------------------------
%e A342757 3  |  9  17  28  42   59 ...
%e A342757 4  | 12  22  37  55   78 ...
%e A342757 5  | 14  27  45  68   96 ...
%e A342757 6  | 17  32  54  81  115 ...
%e A342757 7  | 19  37  62  94  133 ...
%e A342757 ...
%t A342757 T[k_,n_]:= ((1-Mod[k,2])Mod[n,2]+k*(n^2-2*n+2)+n)/2; Table[T[k+3-n,n],{k,3,13},{n,3,k}]//Flatten
%Y A342757 Cf. A016873 (n = 4), A285009 (k = 3), A342719, A342758 (maximum).
%K A342757 nonn,tabl
%O A342757 3,1
%A A342757 _Stefano Spezia_, Mar 21 2021