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

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, 66, 68, 72, 80, 96, 129, 130, 132, 136, 144, 160, 192, 7, 11, 13, 14, 19, 21, 22, 25, 26, 28, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56, 67, 69, 70, 73, 74, 76, 81, 82, 84, 88, 97, 98, 100

Offset: 1

Author

Joe Loughry (loughry(AT)uswest.net)

Keywords

• fini
• full
• nonn

Comments

Subsets are represented by binary vectors.

Examples

			The analogous sequences for smaller k are as follows (rows of A294648 for k >= 1):
for k = 0: 0;
for k = 1: 0, 1;
for k = 2: 0, 1, 2, 3;
for k = 3: 0, 1, 2, 4, 3, 5, 6, 7;
for k = 4: 0, 1, 2, 4, 8, 3, 5, 6, 9, 10, 12, 7, 11, 13, 14, 15;
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.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..256
• J. Loughry, Efficiently Enumerating the Subsets of a Set

Crossrefs

Cf. A003188.

Row 8 of A294648.

Programs

Mathematica

SortBy[Range[0, 255], DigitCount[#, 2, 1] &] (* Paolo Xausa, Mar 31 2025 *)

Extensions

Offset corrected by Sean A. Irvine, May 22 2021