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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).
8
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)
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
Row sums are A001349.
Cf. A263341.
Sequence in context: A145080 A065078 A203989 * A126736 A253257 A127412
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