A066624 Number of 1's in binary expansion of parts in all partitions of n.

0, 1, 3, 7, 13, 23, 41, 65, 102, 156, 234, 340, 495, 697, 982, 1359, 1864, 2523, 3408, 4536, 6022, 7918, 10365, 13457, 17423, 22380, 28666, 36498, 46318, 58466, 73617, 92221, 115236, 143402, 177984, 220086, 271524, 333810, 409490, 500804, 611149, 743728, 903296

Offset: 0

Author

Naohiro Nomoto, Jan 09 2002

Keywords

• easy
• nonn
• base

Examples

			For n = 3: 11 = 10+1 = 1+1+1 [binary expansion of partitions of 3]. a(3) = (two 1's) + (two 1's) + (three 1's), so a(3) = 7.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..8000

Crossrefs

Cf. A000120, A000070, A347060.

Programs

Mathematica

<< DiscreteMath`Combinatorica`; Table[Count[Flatten[IntegerDigits[Partitions[n], 2]], 1], {n, 0, 50}]
Table[Total[Flatten[IntegerDigits[#,2]&/@IntegerPartitions[n]]],{n,0,50}] (* Harvey P. Dale, Mar 29 2022 *)

Extensions

More terms from Vladeta Jovovic and Robert G. Wilson v, Jan 11 2002