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

2,5

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

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

Example

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)

Crossrefs

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

Row sums are A001349.

Cf. A263341.

Sequence in context: A145080 A065078 A203989 * A126736 A253257 A127412

Adjacent sequences: A126741 A126742 A126743 * A126745 A126746 A126747

Keyword

nonn,tabl,hard

Author

N. J. A. Sloane, Feb 18 2007

Extensions

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

Status

approved