A283798 - OEIS

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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.

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

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OFFSET

0,8

LINKS

Table of n, a(n) for n=0..80.

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

Cf. A045655, A283795.

Sequence in context: A132062 A065547 A143333 * A065551 A283797 A059441

Adjacent sequences: A283795 A283796 A283797 * A283799 A283800 A283801

KEYWORD

tabl,nonn

AUTHOR

R. J. Mathar, Mar 16 2017

STATUS

approved