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A343052
Table read by ascending antidiagonals: T(k, n) is the minimum vertex sum in a perimeter-magic k-gon of order n.
1
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
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
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Apr 03 2021
STATUS
approved