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A283798
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.
0
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, 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, 100, 0, 100, 0, 25, 0, 1, 1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 1, 0, 36
OFFSET
0,8
FORMULA
Conjecture: T(n,k) = binomial(n,k) for odd n.
EXAMPLE
The triangle stars 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 4 0 1 rsum= 6
1 5 10 10 5 1 rsum= 32
1 0 9 0 9 0 1 rsum= 20
1 7 21 35 35 21 7 1 rsum= 128
1 0 16 0 44 0 16 0 1 rsum= 78
1 9 36 84 126 126 84 36 9 1 rsum= 512
1 0 25 0 100 0 100 0 25 0 1 rsum= 252
1 11 55 165 330 462 462 330 165 55 11 1 rsum= 2048
1 0 36 0 246 0 420 0 246 0 36 0 1 rsum= 986
1 13 78 286 715 1287 1716 1716 1287 715 286 78 13 1 rsum= 8192
1 0 49 0 441 0 1225 0 1225 0 441 0 49 0 1 rsum= 3432
1 15 105 475 1365 3045 5095 6435 6435 5095 3045 1365 475 105 15 1 rsum= 33072
1 0 64 0 880 0 3136 0 5292 0 3136 0 880 0 64 0 1 rsum= 13454
1 17 136 680 2380 6188 12376 19448 24310 24310 19448 12376 6188 2380 680 136 17 1 rsum= 131072
CROSSREFS
Sequence in context: A132062 A065547 A143333 * A065551 A283797 A059441
KEYWORD
tabl,nonn
AUTHOR
R. J. Mathar, Mar 16 2017
STATUS
approved