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A084269 Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes having chromatic number k, 1 <= k <= n. 10

%I #12 Dec 05 2018 05:14:36

%S 1,0,1,0,1,1,0,3,2,1,0,5,12,3,1,0,17,64,26,4,1,0,44,475,282,46,5,1,0,

%T 182,5036,5009,809,74,6,1,0,730,80947,149551,27794,1940,110,7,1,0,

%U 4032,2010328,7694428,1890221,113272,4125,156,8,1,0,25598,76115143,667036310,248580644,14545025,389583,8040,212,9,1

%N Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes having chromatic number k, 1 <= k <= n.

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

%e Triangle begins:

%e 1;

%e 0, 1;

%e 0, 1, 1;

%e 0, 3, 2, 1;

%e 0, 5, 12, 3, 1;

%e 0, 17, 64, 26, 4, 1;

%e 0, 44, 475, 282, 46, 5, 1;

%e 0, 182, 5036, 5009, 809, 74, 6, 1;

%e 0, 730, 80947, 149551, 27794, 1940, 110, 7, 1;

%e ...

%Y Row sums are A001349.

%Y Columns k=3..7 are A126737, A126738, A126739, A126740, A241702.

%Y Partial row sums include A005142, A076322, A076323, A076324, A076325, A076326, A076327, A076328.

%Y Essentially the same table as A126736.

%Y Cf. A084268 (not necessarily connected), A115597.

%K nonn,tabl

%O 0,8

%A _Eric W. Weisstein_, May 24 2003

%E a(37)-a(66) from _Andrew Howroyd_, Dec 02 2018

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Last modified April 24 20:08 EDT 2024. Contains 371963 sequences. (Running on oeis4.)