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A342757
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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.
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4
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9, 12, 17, 14, 22, 28, 17, 27, 37, 42, 19, 32, 45, 55, 59, 22, 37, 54, 68, 78, 79, 24, 42, 62, 81, 96, 104, 102, 27, 47, 71, 94, 115, 129, 135, 128, 29, 52, 79, 107, 133, 154, 167, 169, 157, 32, 57, 88, 120, 152, 179, 200, 210, 208, 189, 34, 62, 96, 133, 170, 204, 232, 251, 258, 250, 224
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OFFSET
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3,1
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LINKS
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Terrel Trotter, Perimeter-Magic Polygons, Journal of Recreational Mathematics Vol. 7, No. 1, 1974, pp. 14-20 (see equations 10 and 12).
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FORMULA
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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)).
T(k, n) = (n^2/2 - n + 1)*k + n/2 if n is even or both n and k are odd.
T(k, n) = (n^2/2 - n + 1)*k + (n + 1)/2) if n is odd and k is even.
T(k, n) = ((1 - (k mod 2))*(n mod 2) + k*(n^2 - 2*n + 2) + n)/2.
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EXAMPLE
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The array begins:
k\n| 3 4 5 6 7 ...
---+------------------------
3 | 9 17 28 42 59 ...
4 | 12 22 37 55 78 ...
5 | 14 27 45 68 96 ...
6 | 17 32 54 81 115 ...
7 | 19 37 62 94 133 ...
...
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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