OFFSET
0,5
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?
LINKS
P. Zellini, On some properties of circulant matrices, Lin. Alg. Applic. 26 (1979) 31-43
EXAMPLE
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
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. J. Mathar, Mar 16 2017
STATUS
approved