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.
%I A290128 #48 Feb 16 2025 08:33:49
%S A290128 1,2,4,4,8,16,16,18
%N A290128 Domatic number of the halved n-cube graph.
%C A290128 This is the same as the domatic number of the next lower Hamming radius 2 graph. See the Wikipedia link.
%C A290128 a(9) <= 21 because the domination number = 12 and floor(256/12) = 21.
%C A290128 a(10) is known to be 32 as the domination number is 16 and 512/16 is 32; this code is realized by a linear code in the Graham and Sloane paper.
%H A290128 R. L. Graham and N. J. A. Sloane, <a href="http://www.math.ucsd.edu/~ronspubs/85_01_covering_radius.pdf">On the Covering Radius of Codes</a>, IEEE Trans. Inform. Theory, IT-31 (1985), 385-401.
%H A290128 Stan Wagon, <a href="/A290128/a290128_2.txt">Domatic data for halved cube graph</a>
%H A290128 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DomaticNumber.html">Domatic Number</a>
%H A290128 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HalvedCubeGraph.html">Halved Cube Graph</a>
%H A290128 Wikipedia, <a href="https://en.wikipedia.org/wiki/Halved_cube_graph">Halved cube graph</a>
%e A290128 For n=3, two disjoint dominating sets for the Hamming radius-2 graph are {00, 11} and {10 01}, and this means a(2) = 2.
%e A290128 For n = 8, a(8) is the same as the domatic number of the Hamming radius 2 graph built from bit-strings of length 7.
%e A290128 A collection of 18 disjoint dominating sets showing a(8)=18 is:
%e A290128 {0, 18, 47, 57, 84, 107, 111}, {1, 58, 60, 71, 79, 118, 120},
%e A290128 {2, 31, 35, 42, 77, 89, 116}, {3, 7, 11, 12, 112, 125, 126},
%e A290128 {4, 20, 43, 68, 91, 117, 122}, {5, 39, 56, 67, 90, 94, 101},
%e A290128 {6, 53, 55, 73, 88, 98, 108, 123}, {8, 32, 63, 65, 86, 87, 104},
%e A290128 {9, 14, 30, 49, 81, 102, 121}, {10, 24, 40, 50, 69, 119, 127},
%e A290128 {13, 23, 37, 61, 80, 82, 106}, {15, 25, 26, 36, 92, 96, 100, 115},
%e A290128 {16, 21, 52, 59, 78, 99, 105}, {17, 19, 34, 76, 95, 109, 124},
%e A290128 {22, 29, 54, 62, 72, 75, 97}, {27, 38, 44, 64, 85, 110, 113},
%e A290128 {28, 41, 45, 66, 83, 103, 114}, {33, 46, 48, 51, 70, 74, 93},
%e A290128 where the integers from 0 to 127 encode the bit-strings.
%Y A290128 A157887 has the domatic number for Hamming radius 1.
%Y A290128 A029866 has the domination number for these graphs.
%K A290128 nonn,hard,more
%O A290128 1,2
%A A290128 _Stan Wagon_, Jul 20 2017
%E A290128 a(8) = 18 from _Rob Pratt_ and _Stan Wagon_, Jul 26 2017