login
A099199
Number of partitions of n into odd triangular numbers.
1
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
1,3
EXAMPLE
a(8) = #{3+3+1+1, 3+1+1+1+1+1, 1+1+1+1+1+1+1+1} = 3.
MATHEMATICA
Table[Count[IntegerPartitions[n], _?(AllTrue[#, OddQ]&&AllTrue[Sqrt[8#+1], OddQ]&)], {n, 80}] (* Harvey P. Dale, Sep 15 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Oct 04 2004
STATUS
approved