login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A336137 Number of set partitions of the binary indices of n with equal block-sums. 1
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 3, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,8
COMMENTS
A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.
LINKS
EXAMPLE
The a(n) set partitions for n = 7, 59, 119, 367, 127:
{123} {12456} {123567} {1234679} {1234567}
{12}{3} {126}{45} {1236}{57} {12346}{79} {1247}{356}
{15}{24}{6} {156}{237} {1249}{367} {1256}{347}
{17}{26}{35} {1267}{349} {1346}{257}
{169}{2347} {167}{2345}
{16}{25}{34}{7}
The binary indices of 382 are {2,3,4,5,6,7,9}, with equal block-sum set partitions:
{{2,7},{3,6},{4,5},{9}}
{{2,4,6},{3,9},{5,7}}
{{2,7,9},{3,4,5,6}}
{{2,3,4,9},{5,6,7}}
{{2,3,6,7},{4,5,9}}
{{2,4,5,7},{3,6,9}}
{{2,3,4,5,6,7,9}}
so a(382) = 7.
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
Table[Length[Select[sps[bpe[n]], SameQ@@Total/@#&]], {n, 0, 100}]
CROSSREFS
These set partitions are counted by A035470.
The version for twice-partitions is A279787.
The version for partitions of partitions is A305551.
The version for factorizations is A321455.
The version for normal multiset partitions is A326518.
The version for distinct block-sums is A336138.
Set partitions of binary indices are A050315.
Normal multiset partitions with equal lengths are A317583.
Normal multiset partitions with equal averages are A326520.
Multiset partitions with equal block-sums are ranked by A326534.
Sequence in context: A088530 A058060 A338160 * A088323 A003652 A071625
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 12 2020
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)