A334548 Array read by antidiagonals: T(n,k) is the number of n X n symmetric binary matrices with no row sum greater than k.

1, 1, 1, 1, 2, 1, 1, 2, 5, 1, 1, 2, 8, 14, 1, 1, 2, 8, 45, 43, 1, 1, 2, 8, 64, 315, 142, 1, 1, 2, 8, 64, 809, 2634, 499, 1, 1, 2, 8, 64, 1024, 13846, 25518, 1850, 1, 1, 2, 8, 64, 1024, 28217, 301262, 280257, 7193, 1, 1, 2, 8, 64, 1024, 32768, 1146419, 8035168, 3434595, 29186, 1

Offset

0,5

Links

Table of n, a(n) for n=0..65.

Formula

T(n,k) = 2^(n*(n+1)/2) = A006125(n+1) for k >= n.

Example

Array begins:
=============================================================
n\k | 0    1      2       3        4         5         6
----|-------------------------------------------------------
  0 | 1    1      1       1        1         1         1 ...
  1 | 1    2      2       2        2         2         2 ...
  2 | 1    5      8       8        8         8         8 ...
  3 | 1   14     45      64       64        64        64 ...
  4 | 1   43    315     809     1024      1024      1024 ...
  5 | 1  142   2634   13846    28217     32768     32768 ...
  6 | 1  499  25518  301262  1146419   1914733   2097152 ...
  7 | 1 1850 280257 8035168 62951431 178499118 254409765 ...
  ...

Crossrefs

Column k=0..9 are A000012, A005425, A139678, A139679, A139680, A139681, A139682, A139683, A139684, A139685.

Cf. A006125, A135589, A333157.

Sequence in context: A127568 A263791 A327722 * A143364 A309522 A336878

Adjacent sequences: A334545 A334546 A334547 * A334549 A334550 A334551

Keyword

nonn,tabl

Author

Andrew Howroyd, May 08 2020

Status

approved