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

1,3

Comments

Subsets are represented by binary vectors.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..256

J. Loughry, Efficiently Enumerating the Subsets of a Set

Formula

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

Example

The analogous sequences for smaller k are as follows:
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.

Crossrefs

Cf. A003188.

Sequence in context: A133024 A243085 A060376 * A270201 A016025 A036161

Adjacent sequences: A047866 A047867 A047868 * A047870 A047871 A047872

Keyword

fini,full,nonn

Author

Joe Loughry (loughry(AT)uswest.net)

Extensions

Offset corrected by Sean A. Irvine, May 22 2021

Status

approved