VOOZH about

URL: https://oeis.org/A342758

⇱ A342758 - OEIS

login
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.
5
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
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
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Mar 21 2021
STATUS
approved