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A332405 Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with upper irredundance number k.

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%I A332405 #10 Feb 16 2025 08:33:59
%S A332405 1,1,1,1,2,1,1,6,3,1,1,13,15,4,1,1,36,83,30,5,1,1,101,582,302,51,6,1,
%T A332405 1,364,6025,5025,843,80,7,1,1,1511,99503,144371,27160,1996,117,8,1,1,
%U A332405 7917,2706030,7441332,1733212,112291,4211,164,9,1
%N A332405 Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with upper irredundance number k.
%C A332405 First differs from A332403 in row 7.
%C A332405 The upper irredundance number of a graph is the maximum size of an irredundant set. For any graph the upper irredundance number is greater than or equal to the upper domination number (A332403).
%H A332405 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrredundantSet.html">Irredundant Set</a>
%e A332405 Triangle begins:
%e A332405   1;
%e A332405   1,    1;
%e A332405   1,    2,       1;
%e A332405   1,    6,       3,       1;
%e A332405   1,   13,      15,       4,       1;
%e A332405   1,   36,      83,      30,       5,      1;
%e A332405   1,  101,     582,     302,      51,      6,    1;
%e A332405   1,  364,    6025,    5025,     843,     80,    7,   1;
%e A332405   1, 1511,   99503,  144371,   27160,   1996,  117,   8, 1;
%e A332405   1, 7917, 2706030, 7441332, 1733212, 112291, 4211, 164, 9, 1;
%e A332405   ...
%Y A332405 Row sums are A000088.
%Y A332405 Cf. A263284, A263341, A332402, A332403, A332404.
%K A332405 nonn,tabl
%O A332405 1,5
%A A332405 _Andrew Howroyd_, Feb 11 2020