A343052 Table read by ascending antidiagonals: T(k, n) is the minimum vertex sum in a perimeter-magic k-gon of order n.
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, 15, 10, 6, 60, 45, 40, 28, 24, 15, 12, 6, 66, 55, 45, 36, 28, 21, 15, 10, 6, 84, 66, 60, 45, 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
Offset: 3
Examples
The table begins: k\n| 3 4 5 6 7 ... ---+-------------------- 3 | 6 6 6 6 6 ... 4 | 12 10 12 10 12 ... 5 | 15 15 15 15 15 ... 6 | 24 21 24 21 24 ... 7 | 28 28 28 28 28 ... ...
Links
- Terrel Trotter, Perimeter-Magic Polygons, Journal of Recreational Mathematics Vol. 7, No. 1, 1974, pp. 14-20 (see equations 5 and 7).
Crossrefs
Programs
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Mathematica
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
Formula
O.g.f.: x*(1 + x^2 + y + x*(2 + 3*y))/((1 - x)^3*(1 + x)^2*(1 - y^2)).
E.g.f.: x*((5 + 2*x)*cosh(x + y) - cosh(x - y) + 2*(2 + x)*sinh(x + y))/4.
T(k, n) = k*(1 + k + (n mod 2)*(1 - (k mod 2)))/2.
T(k, 3) = A265225(k-1) (conjectured).