A364068 Triangle T(n,k) read by rows: Number of traceless binary n X n matrices with all row and column sums equal to k, 1<=k<=n.

0, 1, 0, 2, 1, 0, 9, 9, 1, 0, 44, 216, 44, 1, 0, 265, 7570, 7570, 265, 1, 0, 1854, 357435, 1975560, 357435, 1854, 1, 0, 14833, 22040361, 749649145, 749649145, 22040361, 14833, 1, 0, 133496, 1721632024

Offset: 1

Author

R. J. Mathar, Jul 04 2023

Keywords

• nonn
• tabl
• more

Examples

			    0
    1        0
    2        1         0
    9        9         1      0
   44      216        44      1    0
  265     7570      7570    265    1 0
 1854   357435   1975560 357435 1854 1 0
14833 22040361 749649145
		

Crossrefs

Cf. A000166 (k=1), A007107 (k=2), A284989 (see 1st col), A284990 (see 1st col, k=3), A007105 (k=3?), A284991 (see 1st col, k=4), A008300 (any trace)

Formula

T(n,n)=0. (k=n would require a 1 on the diagonal)

T(n,n-1)=1. (1 at all entries but the diagonal)

T(n,n-k) = T(n,k-1). (Flip entries 0<->1 and erase diagonal) - R. J. Mathar, Jul 26 2023