

A091891


Number of partitions of n into parts which are a sum of exactly as many distinct powers of 2 as n has 1's in its binary representation.


5



1, 2, 1, 4, 1, 2, 1, 10, 3, 2, 1, 5, 1, 2, 1, 36, 6, 12, 1, 11, 3, 2, 1, 24, 3, 3, 1, 5, 1, 2, 1, 202, 67, 55, 9, 93, 4, 5, 1, 112, 8, 13, 1, 10, 3, 2, 1, 304, 22, 18, 1, 20, 3, 3, 1, 34, 3, 3, 1, 5, 1, 2, 1, 1828, 1267, 1456, 71, 1629, 77, 100, 2, 2342, 99, 123, 9, 132, 4, 3, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1000


FORMULA

a(A000079(n)) = A018819(n);
a(A018900(n)) = A091889(n);
a(A014311(n)) = A091890(n);
a(A091892(n)) = 1.


EXAMPLE

a(9) = 3 because there are 3 partitions of 9 into parts of size 3, 5, 6, 9 which are the numbers that have two 1's in their binary representations. The 3 partitions are: 9, 6 + 3 and 3 + 3 + 3.  Andrew Howroyd, Apr 20 2021


PROG

(PARI) EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))1, #v)}
a(n) = {EulerT(vector(n, k, hammingweight(k)==hammingweight(n)))[n]} \\ Andrew Howroyd, Apr 20 2021


CROSSREFS

Cf. A000079, A000120, A000041, A018819, A018900, A014311.
Cf. A091889, A091890, A091892, A091893.
Sequence in context: A235872 A100762 A059147 * A258127 A181982 A070194
Adjacent sequences: A091888 A091889 A091890 * A091892 A091893 A091894


KEYWORD

nonn,look


AUTHOR

Reinhard Zumkeller, Feb 10 2004


STATUS

approved



