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Triangle read by rows: T(n,k) is the number of graphs with n vertices and bandwidth k.
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%I #14 Oct 27 2017 10:19:18

%S 1,2,3,1,5,5,1,7,18,8,1,11,60,70,14,1,15,195,580,233,20,1,22,623,4942,

%T 5902,826,30,1,30,1989,41332,165514,62562,3196,44,1

%N Triangle read by rows: T(n,k) is the number of graphs with n vertices and bandwidth k.

%C a(1) = T(1,1) uses the convention that the bandwidth of the singleton graph is 1.

%C Row 1 is of length 1; row n if of length n-1 for n > 1.

%C Row sums give A000088(n).

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GraphBandwidth.html">Graph Bandwidth</a>

%F T(n,1) = A000041(n).

%F T(n,n-1) = 1 for n > 2.

%e Triangle begins:

%e 1

%e 2

%e 3,1

%e 5,5,1

%e 7,18,8,1

%e 11,60,70,14,1

%e 15,195,580,233,20,1

%e 22,623,4942,5902,826,30,1

%Y Cf. A000088 (number of simple graphs on n nodes).

%Y Cf. A000041 (number of partitions of n).

%K nonn,tabf,more

%O 1,2

%A _Eric W. Weisstein_, Oct 25 2017