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A342819 Table read by ascending antidiagonals: T(k, n) is the number of distinct values of the magic constant in a perimeter-magic k-gon of order n.

%I A342819 #5 Mar 23 2021 16:18:48
%S A342819 4,4,7,6,9,10,6,11,12,13,8,13,16,17,16,8,15,18,21,20,19,10,17,22,25,
%T A342819 26,25,22,10,19,24,29,30,31,28,25,12,21,28,33,36,37,36,33,28,12,23,30,
%U A342819 37,40,43,42,41,36,31,14,25,34,41,46,49,50,49,46,41,34,14,27,36,45,50,55,56,57,54,51,44,37
%N A342819 Table read by ascending antidiagonals: T(k, n) is the number of distinct values of the magic constant in a perimeter-magic k-gon of order n.
%H A342819 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 10-13).
%F A342819 O.g.f.: (1 - y + 2*x*(y^2 + y - 1) + x^2*(4*y^2 + y - 3))/((1 - x)^2*(1 + x)*(1 - y)^2*(1 + y)).
%F A342819 E.g.f.: (1 + x*(y - 2))*cosh(x + y) + cosh(y)*sinh(x) + x*(y - 2)*sinh(x + y).
%F A342819 T(k, n) = k*(n - 2) + ((k mod 2) - 1)*(n mod 2) + 1.
%F A342819 T(k, n) = A342758(k, n) - A342757(k, n) + 1.
%e A342819 The table begins:
%e A342819 k\n|  3   4   5   6   7 ...
%e A342819 ---+-------------------
%e A342819 3  |  4   7  10  13  16 ...
%e A342819 4  |  4   9  12  17  20 ...
%e A342819 5  |  6  11  16  21  26 ...
%e A342819 6  |  6  13  18  25  30 ...
%e A342819 7  |  8  15  22  29  36 ...
%e A342819 ...
%t A342819 T[k_,n_]:=k(n-2)+(Mod[k,2]-1)Mod[n,2]+1;Table[T[k+3-n,n],{k,3,14},{n,3,k}]//Flatten
%Y A342819 Cf. A005408 (n = 4), A016813 (n = 6), A016921 (n = 8), A017077 (n = 10), A146951 (n = 7), A238290 (n = 9), A342757, A342758.
%K A342819 nonn,tabl
%O A342819 3,1
%A A342819 _Stefano Spezia_, Mar 22 2021