A343052 Table read by ascending antidiagonals: T(k, n) is the minimum vertex sum in a perimeter-magic k-gon of order n.

6, 12, 6, 15, 10, 6, 24, 15, 12, 6, 28, 21, 15, 10, 6, 40, 28, 24, 15, 12, 6, 45, 36, 28, 21, 15, 10, 6, 60, 45, 40, 28, 24, 15, 12, 6, 66, 55, 45, 36, 28, 21, 15, 10, 6, 84, 66, 60, 45, 40, 28, 24, 15, 12, 6, 91, 78, 66, 55, 45, 36, 28, 21, 15, 10, 6, 112, 91, 84, 66, 60, 45, 40, 28, 24, 15, 12, 6

Offset

3,1

Links

Table of n, a(n) for n=3..80.

Terrel Trotter, Perimeter-Magic Polygons, Journal of Recreational Mathematics Vol. 7, No. 1, 1974, pp. 14-20 (see equations 5 and 7).

Formula

O.g.f.: x*(1 + x^2 + y + x*(2 + 3*y))/((1 - x)^3*(1 + x)^2*(1 - y^2)).

E.g.f.: x*((5 + 2*x)*cosh(x + y) - cosh(x - y) + 2*(2 + x)*sinh(x + y))/4.

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

T(k, 3) = A265225(k-1) (conjectured).

Example

The table begins:
k\n|   3   4   5   6   7 ...
---+--------------------
3  |   6   6   6   6   6 ...
4  |  12  10  12  10  12 ...
5  |  15  15  15  15  15 ...
6  |  24  21  24  21  24 ...
7  |  28  28  28  28  28 ...
...

Mathematica

T[k_, n_]:=k(1+k+Mod[n, 2](1-Mod[k, 2]))/2; Table[T[k+3-n, n], {k, 3, 14}, {n, 3, k}]//Flatten

Crossrefs

Cf. A000217 (n = 4), A010722 (k = 3), A010854 (k = 5), A010867 (k = 7), A265225, A343053 (maximum).

Sequence in context: A322214 A315775 A315776 * A050496 A262617 A303226

Adjacent sequences: A343049 A343050 A343051 * A343053 A343054 A343055

Keyword

nonn,tabl

Author

Stefano Spezia, Apr 03 2021

Status

approved