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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.
2

%I #11 Jul 26 2023 06:11:21

%S 0,1,0,2,1,0,9,9,1,0,44,216,44,1,0,265,7570,7570,265,1,0,1854,357435,

%T 1975560,357435,1854,1,0,14833,22040361,749649145,749649145,22040361,

%U 14833,1,0,133496,1721632024

%N 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.

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

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

%F T(n,n-k) = T(n,k-1). (Flip entries 0<->1 and erase diagonal) - _R. J. Mathar_, Jul 26 2023

%e 0

%e 1 0

%e 2 1 0

%e 9 9 1 0

%e 44 216 44 1 0

%e 265 7570 7570 265 1 0

%e 1854 357435 1975560 357435 1854 1 0

%e 14833 22040361 749649145

%Y 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)

%K nonn,tabl,more

%O 1,4

%A _R. J. Mathar_, Jul 04 2023