cp's OEIS Frontend

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

%I A261816 #26 Nov 26 2015 08:51:56
%S A261816 1,0,1,477,160845292
%N A261816 Number of basic semimagic squares of order n that can be formed from the numbers 1, ..., n^2.
%C A261816 In a basic semimagic square the entry in row 1, column 1, is smaller than the other entries.
%C A261816 Moreover, in a basic semimagic square of order n with n >= 3:
%C A261816 a) the entry in row 1, column 2, is smaller than the entry in row 2, column 1
%C A261816 b) every entry in row 1, column 1 < c < n, is smaller than the entry in row 1, column c + 1
%C A261816 c) every entry in row 1 < r < n, column 1, is smaller than the entry in row r + 1, column 1
%C A261816 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).
%H A261816 Arkadiusz Wesolowski, <a href="/A261816/a261816.txt">The solutions of the 477 order-4</a>
%H A261816 Wikipedia, <a href="https://en.wikipedia.org/wiki/Magic_graph">Magic graph</a>
%H A261816 <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>
%F A261816 a(n) = A261815(n)/A048617(n) for n > 1.
%e A261816 An illustration of the unique basic semimagic square of order 3:
%e A261816 |---|---|---|
%e A261816 | 1 | 5 | 9 |
%e A261816 |---|---|---|
%e A261816 | 6 | 7 | 2 |
%e A261816 |---|---|---|
%e A261816 | 8 | 3 | 4 |
%e A261816 |---|---|---|
%Y A261816 Cf. A048617, A261815.
%K A261816 nonn,hard,more
%O A261816 1,4
%A A261816 _Arkadiusz Wesolowski_, Nov 18 2015