cp's OEIS Frontend

A047869 Subsets of an 8-element set in order by number of elements in each subset.

%I A047869 #34 Mar 31 2025 11:30:41
%S A047869 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 A047869 66,68,72,80,96,129,130,132,136,144,160,192,7,11,13,14,19,21,22,25,26,
%U A047869 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 A047869 Subsets of an 8-element set in order by number of elements in each subset.
%C A047869 Subsets are represented by binary vectors.
%H A047869 Sean A. Irvine, <a href="/A047869/b047869.txt">Table of n, a(n) for n = 1..256</a>
%H A047869 J. Loughry, <a href="https://citeseerx.ist.psu.edu/pdf/4c85838527b87815e04206ccc92d0e445f1e6fc1">Efficiently Enumerating the Subsets of a Set</a>
%e A047869 The analogous sequences for smaller k are as follows (rows of A294648 for k >= 1):
%e A047869 for k = 0: 0;
%e A047869 for k = 1: 0, 1;
%e A047869 for k = 2: 0, 1, 2, 3;
%e A047869 for k = 3: 0, 1, 2, 4, 3, 5, 6, 7;
%e A047869 for k = 4: 0, 1, 2, 4, 8, 3, 5, 6, 9, 10, 12, 7, 11, 13, 14, 15;
%e A047869 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.
%t A047869 SortBy[Range[0, 255], DigitCount[#, 2, 1] &] (* _Paolo Xausa_, Mar 31 2025 *)
%Y A047869 Cf. A003188.
%Y A047869 Row 8 of A294648.
%K A047869 fini,full,nonn
%O A047869 1,3
%A A047869 Joe Loughry (loughry(AT)uswest.net)
%E A047869 Offset corrected by _Sean A. Irvine_, May 22 2021