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.
1, 0, 0, 0, 612, 22411, 0
Offset: 1
Examples
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
.
Links
- Donghwi Park, Source code for a(4)~a(6)
Formula
a(n) = 0 if n is a multiple of 4 minus 1.
Comments