A283797 Triangle T(n,k) read by rows: The number of q-circulant n X n {0,1}-matrices where each column sum, each row sum and the trace equal k.

1, 1, 1, 1, 0, 1, 1, 3, 3, 1, 1, 0, 8, 0, 1, 1, 15, 30, 30, 15, 1, 1, 0, 15, 0, 15, 0, 1, 1, 35, 105, 175, 175, 105, 35, 1, 1, 0, 64, 0, 192, 0, 64, 0, 1, 1, 27, 108, 390, 378, 378, 390, 108, 27, 1, 1, 0, 135, 0, 570, 0, 570, 0, 135, 0, 1, 1, 99, 495, 1485, 2970, 4158, 4158, 2970, 1485, 495, 99, 1, 1, 0, 72, 0

Offset: 0

Author

R. J. Mathar, Mar 16 2017

Keywords

• tabl
• nonn

Comments

Obtained from A283795 by selecting the circulant binary matrices where the trace also equals the row and column sum. These match Ryser's criterion for square binary matrices with equal sums in A283627, but do not need to obey A^2=J.

Apparently T(n,k) =0 for odd k if n is even.

Examples

			The triangle starts in row n=0 with columns 0<=k<=n as
1 rsum= 1
1 1 rsum= 2
1 0 1 rsum= 2
1 3 3 1 rsum= 8
1 0 8 0 1 rsum= 10
1 15 30 30 15 1 rsum= 92
1 0 15 0 15 0 1 rsum= 32
1 35 105 175 175 105 35 1 rsum= 632
1 0 64 0 192 0 64 0 1 rsum= 322
1 27 108 390 378 378 390 108 27 1 rsum= 1808
1 0 135 0 570 0 570 0 135 0 1 rsum= 1412
1 99 495 1485 2970 4158 4158 2970 1485 495 99 1 rsum= 18416
1 0 72 0 762 0 1616 0 762 0 72 0 1 rsum= 3286
1 143 858 3146 7865 14157 18876 18876 14157 7865 3146 858 143 1 rsum= 90092
		

Crossrefs

Cf. A283795, A045655.