cp's OEIS Frontend

A343052 Table read by ascending antidiagonals: T(k, n) is the minimum vertex sum in a perimeter-magic k-gon of order n.

%I A343052 #6 Apr 04 2021 01:00:05
%S A343052 6,12,6,15,10,6,24,15,12,6,28,21,15,10,6,40,28,24,15,12,6,45,36,28,21,
%T A343052 15,10,6,60,45,40,28,24,15,12,6,66,55,45,36,28,21,15,10,6,84,66,60,45,
%U A343052 40,28,24,15,12,6,91,78,66,55,45,36,28,21,15,10,6,112,91,84,66,60,45,40,28,24,15,12,6
%N A343052 Table read by ascending antidiagonals: T(k, n) is the minimum vertex sum in a perimeter-magic k-gon of order n.
%H A343052 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 5 and 7).
%F A343052 O.g.f.: x*(1 + x^2 + y + x*(2 + 3*y))/((1 - x)^3*(1 + x)^2*(1 - y^2)).
%F A343052 E.g.f.: x*((5 + 2*x)*cosh(x + y) - cosh(x - y) + 2*(2 + x)*sinh(x + y))/4.
%F A343052 T(k, n) = k*(1 + k + (n mod 2)*(1 - (k mod 2)))/2.
%F A343052 T(k, 3) = A265225(k-1) (conjectured).
%e A343052 The table begins:
%e A343052 k\n|   3   4   5   6   7 ...
%e A343052 ---+--------------------
%e A343052 3  |   6   6   6   6   6 ...
%e A343052 4  |  12  10  12  10  12 ...
%e A343052 5  |  15  15  15  15  15 ...
%e A343052 6  |  24  21  24  21  24 ...
%e A343052 7  |  28  28  28  28  28 ...
%e A343052 ...
%t A343052 T[k_,n_]:=k(1+k+Mod[n,2](1-Mod[k,2]))/2; Table[T[k+3-n,n],{k,3,14},{n,3,k}]//Flatten
%Y A343052 Cf. A000217 (n = 4), A010722 (k = 3), A010854 (k = 5), A010867 (k = 7), A265225, A343053 (maximum).
%K A343052 nonn,tabl
%O A343052 3,1
%A A343052 _Stefano Spezia_, Apr 03 2021