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