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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).

%I A126744 #14 Feb 20 2020 11:40:34
%S A126744 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,
%T A126744 5339,267,1,7,109,1908,26205,136935,94535,1380,1,8,155,4085,110140,
%U A126744 1696407,7121703,2774240,9832,1,9,211,7992,384209,13779220,209046708,647596643,135794730,90842
%N 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).
%C A126744 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
%H A126744 Andrew Howroyd, <a href="/A126744/b126744.txt">Table of n, a(n) for n = 2..79</a> (rows 2..13 derived from Brendan McKay data in A263341)
%H A126744 Keith M. Briggs, <a href="http://keithbriggs.info/cgt.html">Combinatorial Graph Theory</a>
%e A126744 Triangle begins:
%e A126744 n=...1...2...3...4....5....6.....7......8........9........10
%e A126744 k.------------------------------------------------------------
%e A126744 2|...0...1...1...3....6...19....59....267.....1380......9832 = A024607
%e A126744 3|...0...0...1...2...11...63...477...5339....94535...2774240 = A126745
%e A126744 4|...0...0...0...1....3...25...266...4646...136935...7121703 = A126746
%e A126744 5|...0...0...0...0....1....4....45....785....26205...1696407 = A126747
%e A126744 6|...0...0...0...0....0....1.....5.....73.....1908....110140 = A126748
%e A126744 7|...0...0...0...0....0....0.....1......6......109......4085 = A217987
%e A126744 8|...0...0...0...0....0....0.....0......1........7.......155
%e A126744   ...
%e A126744 From _Andrew Howroyd_, Feb 19 2020: (Start)
%e A126744 As a triangle with columns being clique number >= 2:
%e A126744      1;
%e A126744      1,       1;
%e A126744      3,       2,       1;
%e A126744      6,      11,       3,       1;
%e A126744     19,      63,      25,       4,      1;
%e A126744     59,     477,     266,      45,      5,    1;
%e A126744    267,    5339,    4646,     785,     73,    6,   1;
%e A126744   1380,   94535,  136935,   26205,   1908,  109,   7, 1;
%e A126744   9832, 2774240, 7121703, 1696407, 110140, 4085, 155, 8, 1;
%e A126744   ...
%e A126744 (End)
%Y A126744 Diagonals give A024607, A126745, A126746, A126747, A126748, A217987.
%Y A126744 Row sums are A001349.
%Y A126744 Cf. A263341.
%K A126744 nonn,tabl,hard
%O A126744 2,5
%A A126744 _N. J. A. Sloane_, Feb 18 2007
%E A126744 Terms a(47) and beyond derived from A263341 added by _Andrew Howroyd_, Feb 19 2020