login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A325096 Number of maximal subsets of {1...n} with no binary carries. 17
1, 1, 1, 2, 2, 3, 4, 5, 5, 7, 9, 10, 12, 13, 14, 15, 15, 20, 25, 27, 32, 34, 36, 37, 42, 44, 46, 47, 49, 50, 51, 52, 52, 67, 82, 87, 102, 107, 112, 114, 129, 134, 139, 141, 146, 148, 150, 151, 166, 171, 176, 178, 183, 185, 187, 188, 193, 195, 197, 198, 200, 201 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

A binary carry of two positive integers is an overlap of the positions of 1's in their reversed binary expansion.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..8192

FORMULA

a(2^n - 1) = A000110(n).

EXAMPLE

The a(1) = 1 through a(9) = 7 maximal subsets:

  {1}  {12}  {3}   {34}   {25}   {16}   {7}    {78}    {69}

             {12}  {124}  {34}   {25}   {16}   {168}   {78}

                          {124}  {34}   {25}   {258}   {168}

                                 {124}  {34}   {348}   {249}

                                        {124}  {1248}  {258}

                                                       {348}

                                                       {1248}

MATHEMATICA

binpos[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];

stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}];

maxim[s_]:=Complement[s, Last/@Select[Tuples[s, 2], UnsameQ@@#&&SubsetQ@@#&]];

Table[Length[maxim[Select[Subsets[Range[n]], stableQ[#, Intersection[binpos[#1], binpos[#2]]!={}&]&]]], {n, 0, 10}]

CROSSREFS

Cf. A000110, A019565, A050315, A080572, A247935, A267610, A267700.

Cf. A325095, A325099, A325100, A325101, A325103, A325104, A325107.

Sequence in context: A340276 A340275 A342499 * A261771 A015743 A015755

Adjacent sequences:  A325093 A325094 A325095 * A325097 A325098 A325099

KEYWORD

nonn,look

AUTHOR

Gus Wiseman, Mar 27 2019

EXTENSIONS

a(15)-a(61) from Alois P. Heinz, Mar 28 2019

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 21 06:24 EDT 2021. Contains 345358 sequences. (Running on oeis4.)