A126744 Triangle read by rows: T(n,k) gives number of connected graphs on n nodes with clique number n-k, (n>=2, k=0..n-2).

1, 1, 1, 1, 2, 3, 1, 3, 11, 6, 1, 4, 25, 63, 19, 1, 5, 45, 266, 477, 59, 1, 6, 73, 785, 4646, 5339, 267, 1, 7, 109, 1908, 26205, 136935, 94535, 1380, 1, 8, 155, 4085, 110140, 1696407, 7121703, 2774240, 9832, 1, 9, 211, 7992, 384209, 13779220, 209046708, 647596643, 135794730, 90842

Offset: 2

Author

N. J. A. Sloane, Feb 18 2007

Keywords

• nonn
• tabl
• hard

Comments

This sequence can be derived from A263341 since the number of graphs with clique number <= k is the Euler transform of the number of connected graphs with clique number <= k. - Andrew Howroyd, Feb 19 2020

Examples

			Triangle begins:
n=...1...2...3...4....5....6.....7......8........9........10
k.------------------------------------------------------------
2|...0...1...1...3....6...19....59....267.....1380......9832 = A024607
3|...0...0...1...2...11...63...477...5339....94535...2774240 = A126745
4|...0...0...0...1....3...25...266...4646...136935...7121703 = A126746
5|...0...0...0...0....1....4....45....785....26205...1696407 = A126747
6|...0...0...0...0....0....1.....5.....73.....1908....110140 = A126748
7|...0...0...0...0....0....0.....1......6......109......4085 = A217987
8|...0...0...0...0....0....0.....0......1........7.......155
  ...
From _Andrew Howroyd_, Feb 19 2020: (Start)
As a triangle with columns being clique number >= 2:
     1;
     1,       1;
     3,       2,       1;
     6,      11,       3,       1;
    19,      63,      25,       4,      1;
    59,     477,     266,      45,      5,    1;
   267,    5339,    4646,     785,     73,    6,   1;
  1380,   94535,  136935,   26205,   1908,  109,   7, 1;
  9832, 2774240, 7121703, 1696407, 110140, 4085, 155, 8, 1;
  ...
(End)
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 2..79 (rows 2..13 derived from Brendan McKay data in A263341)
• Keith M. Briggs, Combinatorial Graph Theory

Crossrefs

Diagonals give A024607, A126745, A126746, A126747, A126748, A217987.

Row sums are A001349.

Cf. A263341.

Extensions

Terms a(47) and beyond derived from A263341 added by Andrew Howroyd, Feb 19 2020