A342757 - OEIS

%I #7 Mar 23 2021 16:18:31

%S 9,12,17,14,22,28,17,27,37,42,19,32,45,55,59,22,37,54,68,78,79,24,42,

%T 62,81,96,104,102,27,47,71,94,115,129,135,128,29,52,79,107,133,154,

%U 167,169,157,32,57,88,120,152,179,200,210,208,189,34,62,96,133,170,204,232,251,258,250,224

%N Array read by ascending antidiagonals: T(k, n) is the minimum value of the magic constant in a perimeter-magic k-gon of order n.

%H Terrel Trotter, <a href="https://web.archive.org/web/20070106085340/http://www.trottermath.net/simpleops/pmp.html">Perimeter-Magic Polygons</a>, Journal of Recreational Mathematics Vol. 7, No. 1, 1974, pp. 14-20 (see equations 10 and 12).

%F G.f.: (x^2*(-3*y^3 + 2*y - 1) - x*(2*y^3 + y^2 - 2*y + 1) + (y - 1)*y)/((x - 1)^2*(x + 1)*(y - 1)^3*(y + 1)).

%F T(k, n) = (n^2/2 - n + 1)*k + n/2 if n is even or both n and k are odd.

%F T(k, n) = (n^2/2 - n + 1)*k + (n + 1)/2) if n is odd and k is even.

%F T(k, n) = ((1 - (k mod 2))*(n mod 2) + k*(n^2 - 2*n + 2) + n)/2.

%e The array begins:

%e k\n|  3   4   5   6    7 ...

%e ---+------------------------

%e 3  |  9  17  28  42   59 ...

%e 4  | 12  22  37  55   78 ...

%e 5  | 14  27  45  68   96 ...

%e 6  | 17  32  54  81  115 ...

%e 7  | 19  37  62  94  133 ...

%e ...

%t T[k_,n_]:= ((1-Mod[k,2])Mod[n,2]+k*(n^2-2*n+2)+n)/2; Table[T[k+3-n,n],{k,3,13},{n,3,k}]//Flatten

%Y Cf. A016873 (n = 4), A285009 (k = 3), A342719, A342758 (maximum).

%K nonn,tabl

%O 3,1

%A _Stefano Spezia_, Mar 21 2021