A343053 Table read by ascending antidiagonals: T(k, n) is the maximum vertex sum in a perimeter-magic k-gon of order n.
15, 24, 24, 40, 42, 33, 54, 65, 56, 42, 77, 93, 90, 74, 51, 96, 126, 126, 115, 88, 60, 126, 164, 175, 165, 140, 106, 69, 150, 207, 224, 224, 198, 165, 120, 78, 187, 255, 288, 292, 273, 237, 190, 138, 87, 216, 308, 350, 369, 352, 322, 270, 215, 152, 96, 260, 366, 429, 455, 450, 420, 371, 309, 240, 170, 105
Offset: 3
Examples
The table begins: k\n| 3 4 5 6 7 ... ---+------------------------ 3 | 15 24 33 42 51 ... 4 | 24 42 56 74 88 ... 5 | 40 65 90 115 140 ... 6 | 54 93 126 165 198 ... 7 | 77 126 175 224 273 ... ...
Links
- Terrel Trotter, Perimeter-Magic Polygons, Journal of Recreational Mathematics Vol. 7, No. 1, 1974, pp. 14-20 (see equations 6 and 8).
Programs
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Mathematica
T[k_,n_]:=k(1+k(2n-3)-Mod[n,2](1-Mod[k,2]))/2; Table[T[k+3-n,n],{k,3,14},{n,3,k}]//Flatten
Formula
T(k, n) = k*(1 + k*(2n - 3) - (n mod 2)*(1 - (k mod 2)))/2.
T(n, n) = A059270(n-1).