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

3,1

Links

Table of n, a(n) for n=3..68.

Terrel Trotter, Perimeter-Magic Polygons, Journal of Recreational Mathematics Vol. 7, No. 1, 1974, pp. 14-20 (see equations 6 and 8).

Formula

T(k, n) = k*(1 + k*(2n - 3) - (n mod 2)*(1 - (k mod 2)))/2.

T(n, n) = A059270(n-1).

Example

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 ...
...

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

Crossrefs

Cf. A005475 (n = 4), A022267 (n = 6), A059270, A179805 (k = 3), A343052 (minimum).

Sequence in context: A166657 A059144 A274339 * A114436 A114558 A035408

Adjacent sequences: A343050 A343051 A343052 * A343054 A343055 A343056

Keyword

nonn,tabl

Author

Stefano Spezia, Apr 03 2021

Status

approved