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%I #19 May 23 2021 02:58:21
%S 0,1,2,4,8,16,32,64,128,3,5,6,9,10,12,17,18,20,24,33,34,36,40,48,65,
%T 66,68,72,80,96,129,130,132,136,144,160,192,7,11,13,14,19,21,22,25,26,
%U 28,35,37,38,41,42,44,49,50,52,56,67,69,70,73,74,76,81,82,84,88,97,98,100
%N Subsets of an 8-element set in order by number of elements in each subset.
%C Subsets are represented by binary vectors.
%H Sean A. Irvine, <a href="/A047869/b047869.txt">Table of n, a(n) for n = 1..256</a>
%H J. Loughry, <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.18.6972&rep=rep1&type=pdf">Efficiently Enumerating the Subsets of a Set</a>
%F Main diagonal of the array defined by T(0, j) = j+1 for j>=0, T(i, 0) = i+1 for i>=0, T(i, j) = T(i-1, j-1) + T(i-1, j) + 7; a(n) = 2^(n-1)*(n+16) - 7. - _Benoit Cloitre_, Jun 17 2003
%e The analogous sequences for smaller k are as follows:
%e for k = 0: 0;
%e for k = 1: 0, 1;
%e for k = 2: 0, 1, 2, 3;
%e for k = 3: 0, 1, 2, 4, 3, 5, 6, 7;
%e for k = 4: 0, 1, 2, 4, 8, 3, 5, 6, 9, 10, 12, 7, 11, 13, 14, 15;
%e for k = 5: 0, 1, 2, 4, 8, 16, 3, 5, 6, 9, 10, 12, 17, 18, 20, 24, 7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 15, 23, 27, 29, 30, 31.
%Y Cf. A003188.
%K fini,full,nonn
%O 1,3
%A Joe Loughry (loughry(AT)uswest.net)
%E Offset corrected by _Sean A. Irvine_, May 22 2021
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