A162931 Irregular table which maps each partition of n counted in A162932 to a binary number (converted to decimal).

14, 30, 28, 62, 58, 56, 60, 126, 118, 114, 122, 254, 112, 116, 124, 238, 120, 230, 246, 510, 226, 234, 250, 478, 224, 228, 236, 242, 252, 462, 494, 1022

Offset: 6

Author

Alford Arnold, Jul 17 2009

Keywords

• nonn
• tabf
• base
• less

Comments

The table encodes each partition of n which satisfies the requirements of A162932 into a binary number with run lengths of 1 determined by the frequency of the parts. As many most-significant-bits are set as determined by the run length of the largest part, each run of 1 is terminated by a 0, and missing parts in the partition are represented by consecutive zeros. Each part in the partition and its frequency pick one member of A079946, and the full binary number is a concatenation of these bits. - R. J. Mathar, Jul 13 2012

Examples

			For n=17, the A162932(17)=4 solutions are 2+2+2+2+3+3+3, 2+3+3+3+3+3, 2+3+4+4+4, and 2+5+5+5. These are represented here by
111011110=478 (3 threes give a run length of 3, and four 2's give a run length of 4),
11111010=250 (five 3's give a run length of 5 and one 2 gives a run length of 1),
11101010=234 (three 4's give a run length of 3, one 3 gives a run length of 1 and one 2 gives another run length of 1),
and 11100010=226 (three 5's give a run length of 3, missing 4 and 3 give two run lengths of zero, one 2 give one run length of 1),
then sorted into row 17. - _R. J. Mathar_, Jul 13 2012
A162932 begins 1 0 1 1 1 1 3 1 3 4 4 4 8 6 ... so the table begins
14
.
30
28
62
58
56,60,126
118
114,122,254
112,116,124,238
120,230,246,510
226,234,250,478
224,228,236,242,252,462,494,1022
		

Crossrefs

A162932 (number of entries per row). A079946