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

3,1

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 11 and 13).

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.

Example

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 ...
...

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

Crossrefs

Cf. A017005 (n = 4), A135503 (diagonal), A341740 (k = 3), A342719, A342757 (minimum).

Sequence in context: A259040 A158190 A122040 * A274550 A253235 A050480

Adjacent sequences: A342755 A342756 A342757 * A342759 A342760 A342761

Keyword

nonn,tabl

Author

Stefano Spezia, Mar 21 2021

Status

approved