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A356643
a(n) is the number of order-n magic triangles composed of the numbers from 1 to n(n+1)/2 in which the sum of the k-th row and the (n-k)-th row is same for all k and all three directions, counted up to rotations and reflections.
2
1, 0, 0, 0, 612, 22411, 0
OFFSET
1,5
COMMENTS
The magic sum is n*(n*(n + 1)/2 + 1)/2.
FORMULA
a(n) = 0 if n is a multiple of 4 minus 1.
EXAMPLE
a(1) is trivially 1.
a(2) is trivially 0.
a(4k-1) for positive integers k is trivially 0 because the magic sums are not integers in these cases.
a(4) is 0.
An example of a solution at n=5:
.
1
15 5
9 4 7
12 6 8 13
3 11 2 10 14
.
An example of a solution at n=6:
.
5
19 16
12 1 20
9 6 10 8
18 11 7 21 2
3 17 13 4 14 15
.
CROSSREFS
Cf. A000217 (triangular number), A006052 (magic square), A004767, A342467, A355119.
Sequence in context: A232119 A232417 A250997 * A022049 A107513 A151592
KEYWORD
nonn,more
AUTHOR
Donghwi Park, Aug 19 2022
STATUS
approved