A283798 - OEIS

%I #11 Nov 05 2021 10:22:36

%S 1,1,1,1,0,1,1,3,3,1,1,0,4,0,1,1,5,10,10,5,1,1,0,9,0,9,0,1,1,7,21,35,

%T 35,21,7,1,1,0,16,0,44,0,16,0,1,1,9,36,84,126,126,84,36,9,1,1,0,25,0,

%U 100,0,100,0,25,0,1,1,11,55,165,330,462,462,330,165,55,11,1,1,0,36

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

%F Conjecture: T(n,k) = binomial(n,k) for odd n.

%e The triangle stars in row n=0 with columns 0<=k<=n as

%e 1 rsum= 1

%e 1  1 rsum= 2

%e 1  0   1 rsum= 2

%e 1  3   3   1 rsum= 8

%e 1  0   4   0    1 rsum= 6

%e 1  5  10  10    5    1 rsum= 32

%e 1  0   9   0    9    0     1 rsum= 20

%e 1  7  21  35   35   21     7     1 rsum= 128

%e 1  0  16   0   44    0    16     0     1 rsum= 78

%e 1  9  36  84  126  126    84    36     9     1 rsum= 512

%e 1  0  25   0  100    0   100     0    25     0     1 rsum= 252

%e 1 11  55 165  330  462   462   330   165    55    11     1 rsum= 2048

%e 1  0  36   0  246    0   420     0   246     0    36     0 1 rsum= 986

%e 1 13  78 286  715 1287  1716  1716  1287   715   286    78 13 1 rsum= 8192

%e 1  0  49   0  441    0  1225     0  1225     0   441     0 49 0 1 rsum= 3432

%e 1 15 105 475 1365 3045  5095  6435  6435  5095  3045  1365 475 105 15 1 rsum= 33072

%e 1  0  64   0  880    0  3136     0  5292     0  3136     0 880 0 64 0 1 rsum= 13454

%e 1 17 136 680 2380 6188 12376 19448 24310 24310 19448 12376 6188 2380 680 136 17 1 rsum= 131072

%Y Cf. A045655, A283795.

%K tabl,nonn

%O 0,8

%A _R. J. Mathar_, Mar 16 2017