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

0,3

Links

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

Example

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.

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 *)

Crossrefs

Cf. A000120, A000070, A347060.

Sequence in context: A306902 A227121 A078447 * A317783 A061761 A081494

Adjacent sequences: A066621 A066622 A066623 * A066625 A066626 A066627

Keyword

easy,nonn,base

Author

Naohiro Nomoto, Jan 09 2002

Extensions

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

Status

approved