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

1,5

Comments

The magic sum is n*(n*(n + 1)/2 + 1)/2.

Links

Table of n, a(n) for n=1..7.

Donghwi Park, Source code for a(4)~a(6)

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

Adjacent sequences: A356640 A356641 A356642 * A356644 A356645 A356646

Keyword

nonn,more

Author

Donghwi Park, Aug 19 2022

Status

approved