A099199 Number of partitions of n into odd triangular numbers.
1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 7, 7, 7, 9, 9, 9, 12, 12, 12, 15, 15, 15, 18, 18, 18, 22, 22, 22, 26, 26, 26, 31, 31, 31, 36, 36, 36, 42, 42, 42, 50, 50, 50, 58, 58, 58, 67, 67, 67, 76, 77, 77, 87, 88, 88, 100, 101, 101, 114, 115, 115, 130, 131, 131, 146, 148, 148, 164
Offset: 1
Keywords
Examples
a(8) = #{3+3+1+1, 3+1+1+1+1+1, 1+1+1+1+1+1+1+1} = 3.
Programs
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Mathematica
Table[Count[IntegerPartitions[n],?(AllTrue[#,OddQ]&&AllTrue[Sqrt[8#+1],OddQ]&)],{n,80}] (* _Harvey P. Dale, Sep 15 2024 *)