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.

A333159 Triangle read by rows: T(n,k) is the number of non-isomorphic n X n symmetric binary matrices with k ones in every row and column up to permutation of rows and columns.

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%I A333159 #5 Mar 11 2020 18:06:52
%S A333159 1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,2,2,1,1,1,1,4,5,4,1,1,1,1,4,12,12,
%T A333159 4,1,1,1,1,7,31,66,31,7,1,1,1,1,8,90,433,433,90,8,1,1,1,1,12,285,3442,
%U A333159 7937,3442,285,12,1,1,1,1,14,938,30404,171984,171984,30404,938,14,1,1
%N A333159 Triangle read by rows: T(n,k) is the number of non-isomorphic n X n symmetric binary matrices with k ones in every row and column up to permutation of rows and columns.
%C A333159 Rows and columns may be permuted independently. The case that rows and columns must be permuted together is covered by A333161.
%C A333159 T(n,k) is the number of k-regular bicolored graphs on 2n unlabeled nodes which are invariant when the two color classes are exchanged.
%H A333159 Andrew Howroyd, <a href="/A333159/b333159.txt">Table of n, a(n) for n = 0..230</a>
%F A333159 T(n,k) = T(n,n-k).
%e A333159 Triangle begins:
%e A333159   1;
%e A333159   1, 1;
%e A333159   1, 1,  1;
%e A333159   1, 1,  1,   1;
%e A333159   1, 1,  2,   1,    1;
%e A333159   1, 1,  2,   2,    1,    1;
%e A333159   1, 1,  4,   5,    4,    1,    1;
%e A333159   1, 1,  4,  12,   12,    4,    1,   1;
%e A333159   1, 1,  7,  31,   66,   31,    7,   1,  1;
%e A333159   1, 1,  8,  90,  433,  433,   90,   8,  1, 1;
%e A333159   1, 1, 12, 285, 3442, 7937, 3442, 285, 12, 1, 1;
%e A333159   ...
%e A333159 The T(2,1) = 1 matrix is:
%e A333159   [1 0]
%e A333159   [0 1]
%e A333159 .
%e A333159 The T(4,2)= 2 matrices are:
%e A333159   [1 1 0 0]   [1 1 0 0]
%e A333159   [1 1 0 0]   [1 0 1 0]
%e A333159   [0 0 1 1]   [0 1 0 1]
%e A333159   [0 0 1 1]   [0 0 1 1]
%Y A333159 Columns k=0..4 are A000012, A000012, A002865, A000840, A000843.
%Y A333159 Row sums are A333160.
%Y A333159 Central coefficients are A333165.
%Y A333159 Cf. A008327, A122082, A333157, A133687, A333161.
%K A333159 nonn,tabl
%O A333159 0,13
%A A333159 _Andrew Howroyd_, Mar 10 2020