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%I #9 Aug 09 2020 09:19:44
%S 3,2,9,7,19,8,8,56,90,2,16,496,520,12,0,266,8308,3584,284,4,0,45186,
%T 199247,28781,1434,20,0,0,6054148,5637886,301530,10686,914,4,0,0
%N Triangle T(n,k) of the number of unlabeled graphs on n nodes with universal reconstruction number k, 3<=k<=n. URN(G) is the minimum size for which all multisubsets of vertex-deleted subgraphs of G can uniquely reconstruct G up to isomorphism.
%C The (vertex) Reconstruction Conjecture, due to Kelly and Ulam, states that every graph with three or more vertices is reconstructible up to isomorphism given the multiset of vertex deleted subgraphs. Equivalently, every graph has an URN and so sum(k=3,n,T(n,k))==A000088(n) for all n>=3.
%H P. J. Kelly, <a href="https://projecteuclid.org/euclid.pjm/1103043674">A congruence theorem for trees</a>, Pacific J. Math., 7 (1957), 961-968.
%H B. McMullen, <a href="https://www.semanticscholar.org/paper/Graph-reconstruction-numbers-McMullen/09d3f018cdc3feedd30d5ed32ccca9344cc180c4">Graph reconstruction numbers</a>.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Reconstruction_conjecture">Reconstruction conjecture</a>.
%e Triangle begins
%e 3
%e 2 9
%e 7 19 8
%e 8 56 90 2
%e 16 496 520 12 0
%e 266 8308 3584 284 4 0
%e 45186 199247 28781 1434 20 0 0
%e 6054148 5637886 301530 10686 914 4 0 0
%Y Cf. A124002, A000088, A006652-A006655.
%K hard,more,nice,nonn,tabl
%O 3,1
%A _Martin Fuller_, Dec 08 2006
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