cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A283796 Triangle T(n,k) read by rows: the number of symmetric q-circulant n X n {0,1}-matrices where each row and each column sum equals k.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 6, 6, 6, 1, 1, 6, 12, 12, 6, 1, 1, 8, 18, 22, 18, 8, 1, 1, 8, 24, 38, 38, 24, 8, 1, 1, 16, 38, 80, 86, 80, 38, 16, 1, 1, 10, 40, 88, 132, 132, 88, 40, 10, 1, 1, 12, 50, 128, 220, 262, 220, 128, 50, 12, 1, 1, 12, 60, 170, 340, 472, 472, 340, 170, 60, 12, 1
Offset: 0

Views

Author

R. J. Mathar, Mar 16 2017

Keywords

Comments

Obtained by selecting matrices in A283795 which are symmetric, which means where the transpose of the binary matrix equals the matrix.
Is column k=1 the same as A235384?

Examples

			The matrix stars in rows n=0 and columns 0<=k<n as
1 rsum= 1
1 1 rsum= 2
1 2 1 rsum= 4
1 4 4 1 rsum= 10
1 6 6 6 1 rsum= 20
1 6 12 12 6 1 rsum= 38
1 8 18 22 18 8 1 rsum= 76
1 8 24 38 38 24 8 1 rsum= 142
1 16 38 80 86 80 38 16 1 rsum= 356
1 10 40 88 132 132 88 40 10 1 rsum= 542
1 12 50 128 220 262 220 128 50 12 1 rsum= 1084
1 12 60 170 340 472 472 340 170 60 12 1 rsum= 2110
1 24 92 282 586 936 1050 936 586 282 92 24 1 rsum= 4892
1 14 84 292 730 1302 1736 1736 1302 730 292 84 14 1 rsum= 8318

Crossrefs

Cf. A235384, A045655.

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.

Original entry on oeis.org

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
Offset: 0

Views

Author

R. J. Mathar, Mar 16 2017

Keywords

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.

Examples

			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.

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.

Original entry on oeis.org

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

Views

Author

R. J. Mathar, Mar 16 2017

Keywords

Examples

			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.

Formula

Conjecture: T(n,k) = binomial(n,k) for odd n.
Showing 1-3 of 3 results.

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