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A091893
Number of partitions of n into numbers having all the same number of 1's in binary representation.
4
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
1,2
LINKS
EXAMPLE
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.
MATHEMATICA
Table[Count[IntegerPartitions[n], _?(Length[Union[DigitCount[ #, 2, 1]&/@ #]]==1&)], {n, 60}] (* Harvey P. Dale, Aug 23 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Feb 10 2004
STATUS
approved