OFFSET
0,3
FORMULA
EXAMPLE
For n = 4 we have:
------------------------------------
Partitions Number of parts
. which are powers of 2
------------------------------------
4 ..................... 1
3 + 1 ................. 1
2 + 2 ................. 2
2 + 1 + 1 ............. 3
1 + 1 + 1 + 1 ......... 4
------------------------------------
Total ................ 11
So a(4) = 11.
MATHEMATICA
nmax = 43; CoefficientList[Series[Sum[x^(2^k)/(1 - x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}]/Product[(1 - x^j), {j, 1, nmax}], {x, 0, nmax}], x]
Table[Sum[IntegerExponent[2 k, 2] PartitionsP[n - k], {k, 1, n}], {n, 0, 43}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 06 2021
STATUS
approved