A283797 - OEIS

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A283797

Triangle T(n,k) read by rows: The number of 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, 8, 0, 1, 1, 15, 30, 30, 15, 1, 1, 0, 15, 0, 15, 0, 1, 1, 35, 105, 175, 175, 105, 35, 1, 1, 0, 64, 0, 192, 0, 64, 0, 1, 1, 27, 108, 390, 378, 378, 390, 108, 27, 1, 1, 0, 135, 0, 570, 0, 570, 0, 135, 0, 1, 1, 99, 495, 1485, 2970, 4158, 4158, 2970, 1485, 495, 99, 1, 1, 0, 72, 0

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OFFSET

0,8

COMMENTS

Obtained from A283795 by selecting the circulant binary matrices where the trace also equals the row and column sum. These match Ryser's criterion for square binary matrices with equal sums in A283627, but do not need to obey A^2=J.

Apparently T(n,k) =0 for odd k if n is even.

LINKS

Table of n, a(n) for n=0..81.

EXAMPLE

The triangle starts 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 8 0 1 rsum= 10

1 15 30 30 15 1 rsum= 92

1 0 15 0 15 0 1 rsum= 32

1 35 105 175 175 105 35 1 rsum= 632

1 0 64 0 192 0 64 0 1 rsum= 322

1 27 108 390 378 378 390 108 27 1 rsum= 1808

1 0 135 0 570 0 570 0 135 0 1 rsum= 1412

1 99 495 1485 2970 4158 4158 2970 1485 495 99 1 rsum= 18416

1 0 72 0 762 0 1616 0 762 0 72 0 1 rsum= 3286

1 143 858 3146 7865 14157 18876 18876 14157 7865 3146 858 143 1 rsum= 90092

CROSSREFS

Cf. A283795, A045655.

Sequence in context: A143333 A283798 A065551 * A059441 A186028 A225054

Adjacent sequences: A283794 A283795 A283796 * A283798 A283799 A283800

KEYWORD

tabl,nonn

AUTHOR

R. J. Mathar, Mar 16 2017

STATUS

approved