cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

Original entry on oeis.org

1, 0, 0, 0, 612, 22411, 0
Offset: 1

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Author

Donghwi Park, Aug 19 2022

Keywords

Comments

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

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
.
		

Crossrefs

Cf. A000217 (triangular number), A006052 (magic square), A004767, A342467, A355119.

Formula

a(n) = 0 if n is a multiple of 4 minus 1.