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.

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, 42, 126, 210, 210, 126, 42, 1, 1, 32, 136, 224, 350, 224, 136, 32, 1, 1, 54, 216, 546, 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

Offset: 0

Author

R. J. Mathar, Mar 16 2017

Keywords

• nonn
• tabl

Comments

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.

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.

The number of 1-circulant matrices with k zeros in each row and each column is apparently given by Pascal's Triangle.

Is the column k=1 given by A002618?

Examples

			The triangle starts in row n=0 and column k=0 as:
1 rsum= 1
1 1 rsum= 2
1 2 1 rsum= 4
1 6 6 1 rsum= 14
1 8 14 8 1 rsum= 32
1 20 40 40 20 1 rsum= 122
1 12 42 44 42 12 1 rsum= 154
1 42 126 210 210 126 42 1 rsum= 758
1 32 136 224 350 224 136 32 1 rsum= 1136
1 54 216 546 756 756 546 216 54 1 rsum= 3146
		

Links

• P. Zellini, On some properties of circulant matrices, Lin. Alg. Applic. 26 (1979) 31-43

Crossrefs

Cf. A045655.