cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A084269 #13 Feb 16 2025 08:32:49
%S A084269 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 A084269 182,5036,5009,809,74,6,1,0,730,80947,149551,27794,1940,110,7,1,0,
%U A084269 4032,2010328,7694428,1890221,113272,4125,156,8,1,0,25598,76115143,667036310,248580644,14545025,389583,8040,212,9,1
%N 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.
%H A084269 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/n-ChromaticGraph.html">n-Chromatic Graph</a>
%e A084269 Triangle begins:
%e A084269   1;
%e A084269   0,   1;
%e A084269   0,   1,     1;
%e A084269   0,   3,     2,      1;
%e A084269   0,   5,    12,      3,     1;
%e A084269   0,  17,    64,     26,     4,    1;
%e A084269   0,  44,   475,    282,    46,    5,   1;
%e A084269   0, 182,  5036,   5009,   809,   74,   6, 1;
%e A084269   0, 730, 80947, 149551, 27794, 1940, 110, 7, 1;
%e A084269   ...
%Y A084269 Row sums are A001349.
%Y A084269 Columns k=3..7 are A126737, A126738, A126739, A126740, A241702.
%Y A084269 Partial row sums include A005142, A076322, A076323, A076324, A076325, A076326, A076327, A076328.
%Y A084269 Essentially the same table as A126736.
%Y A084269 Cf. A084268 (not necessarily connected), A115597.
%K A084269 nonn,tabl
%O A084269 0,8
%A A084269 _Eric W. Weisstein_, May 24 2003
%E A084269 a(37)-a(66) from _Andrew Howroyd_, Dec 02 2018