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A283795 Triangle T(n,k) read by rows: the number of q-circulant n X n {0,1}-matrices where each row sum and each column sum equals k.

%I A283795 #10 Mar 16 2017 17:35:45
%S A283795 1,1,1,1,2,1,1,6,6,1,1,8,14,8,1,1,20,40,40,20,1,1,12,42,44,42,12,1,1,
%T A283795 42,126,210,210,126,42,1,1,32,136,224,350,224,136,32,1,1,54,216,546,
%U A283795 756,756,546,216,54,1,1,40,260,480,1200,1032,1200,480,260,40,1,1,110,550,1650,3300,4620,4620,3300,1650,550,110,1,1,48,324,992,2538,3168
%N A283795 Triangle T(n,k) read by rows: the number of q-circulant n X n {0,1}-matrices where each row sum and each column sum equals k.
%C A283795 q-circulant matrices are constructed by fixing the first row and obtaining the remaining n-1 rows by circularly shifting values by q columns, any q from 0 to n-1.
%C A283795 The triangle is symmetric in each row because flipping 1's and 0's in a matrix gives also a circulant matrix with n-k ones in each row and column.
%C A283795 The number of 1-circulant matrices with k zeros in each row and each column is apparently given by Pascal's Triangle.
%C A283795 Is the column k=1 given by A002618?
%H A283795 P. Zellini, <a href="http://dx.doi.org/10.1016/0024-3795(79)90170-8">On some properties of circulant matrices</a>, Lin. Alg. Applic. 26 (1979) 31-43
%e A283795 The triangle starts in row n=0 and column k=0 as:
%e A283795 1 rsum= 1
%e A283795 1 1 rsum= 2
%e A283795 1 2 1 rsum= 4
%e A283795 1 6 6 1 rsum= 14
%e A283795 1 8 14 8 1 rsum= 32
%e A283795 1 20 40 40 20 1 rsum= 122
%e A283795 1 12 42 44 42 12 1 rsum= 154
%e A283795 1 42 126 210 210 126 42 1 rsum= 758
%e A283795 1 32 136 224 350 224 136 32 1 rsum= 1136
%e A283795 1 54 216 546 756 756 546 216 54 1 rsum= 3146
%Y A283795 Cf. A045655.
%K A283795 nonn,tabl
%O A283795 0,5
%A A283795 _R. J. Mathar_, Mar 16 2017