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A343053 Table read by ascending antidiagonals: T(k, n) is the maximum vertex sum in a perimeter-magic k-gon of order n. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 3 15:11 EDT 2021. Contains 346438 sequences. (Running on oeis4.)