A261816 Number of basic semimagic squares of order n that can be formed from the numbers 1, ..., n^2.

1, 0, 1, 477, 160845292

Offset

1,4

Comments

In a basic semimagic square the entry in row 1, column 1, is smaller than the other entries.

Moreover, in a basic semimagic square of order n with n >= 3:

a) the entry in row 1, column 2, is smaller than the entry in row 2, column 1

b) every entry in row 1, column 1 < c < n, is smaller than the entry in row 1, column c + 1

c) every entry in row 1 < r < n, column 1, is smaller than the entry in row r + 1, column 1

For n > 1, the total number of semimagic squares of order n that can be formed from the numbers 1, ..., n^2 is a(n)*A048617(n) = A261815(n).

Links

Table of n, a(n) for n=1..5.

Arkadiusz Wesolowski, The solutions of the 477 order-4

Wikipedia, Magic graph

Index entries for sequences related to magic squares

Formula

a(n) = A261815(n)/A048617(n) for n > 1.

Example

An illustration of the unique basic semimagic square of order 3:
|---|---|---|
| 1 | 5 | 9 |
|---|---|---|
| 6 | 7 | 2 |
|---|---|---|
| 8 | 3 | 4 |
|---|---|---|

Crossrefs

Cf. A048617, A261815.

Sequence in context: A325822 A224453 A227706 * A352265 A020375 A031788

Adjacent sequences: A261813 A261814 A261815 * A261817 A261818 A261819

Keyword

nonn,hard,more

Author

Arkadiusz Wesolowski, Nov 18 2015

Status

approved