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.
12, 15, 23, 19, 30, 37, 22, 37, 48, 54, 26, 44, 60, 71, 74, 29, 51, 71, 88, 97, 97, 33, 58, 83, 105, 121, 128, 123, 36, 65, 94, 122, 144, 159, 162, 152, 40, 72, 106, 139, 168, 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
Offset: 3
Examples
The array begins: k\n| 3 4 5 6 7 ... ---+--------------------- 3 | 12 23 37 54 74 ... 4 | 15 30 48 71 97 ... 5 | 19 37 60 88 121 ... 6 | 22 44 71 105 144 ... 7 | 26 51 83 122 168 ... ...
Links
- Terrel Trotter, Perimeter-Magic Polygons, Journal of Recreational Mathematics Vol. 7, No. 1, 1974, pp. 14-20 (see equations 11 and 13).
Programs
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Mathematica
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
Formula
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)).
T(k, n) = (n^2/2 - 1)*k + n/2 if n is even or both n and k are odd.
T(k, n) = (n^2/2 - 1)*k + (n - 1)/2 if n is odd and k is even.
T(k, n) = (n + k*(n^2 - 2) + ((k mod 2) - 1)*(n mod 2))/2.