A091893 Number of partitions of n into numbers having all the same number of 1's in binary representation.

1, 2, 3, 4, 5, 8, 7, 11, 13, 16, 17, 25, 23, 31, 35, 40, 42, 59, 53, 72, 79, 87, 91, 119, 114, 140, 151, 171, 178, 219, 203, 257, 275, 296, 319, 382, 364, 435, 467, 511, 533, 635, 609, 721, 764, 826, 865, 1011, 994, 1141, 1203, 1301, 1371, 1571, 1541, 1773

Offset: 1

Author

Reinhard Zumkeller, Feb 10 2004

Keywords

• nonn

Examples

			n=30 -> '11110', a(30) = (#partitions into numbers with 1 binary 1) + (#partitions into numbers with 2 binary 1's) + (#partitions into numbers with 3 binary 1's) + (#partitions into numbers with 4 binary 1's) + (#partitions into numbers with 5 binary 1's) = A018819(30) + A091889(30) + A091890(30) + #{'11110','1111'+'1111'} + #empty = 166 + 50 + 1 + 2 + 0 = 219.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000120, A000041, A091889, A091890, A091891.

Programs

Mathematica

Table[Count[IntegerPartitions[n],?(Length[Union[DigitCount[ #,2,1]&/@ #]]==1&)],{n,60}] (* _Harvey P. Dale, Aug 23 2020 *)