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!)
A355146 Triangle read by rows: T(n,k) is the number of subsets of {1,...,n} of cardinality k in which every pair of elements is coprime; n >= 0, 0 <= k <= A036234(n). 0
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 5, 2, 1, 5, 9, 7, 2, 1, 6, 11, 8, 2, 1, 7, 17, 19, 10, 2, 1, 8, 21, 25, 14, 3, 1, 9, 27, 37, 24, 6, 1, 10, 31, 42, 26, 6, 1, 11, 41, 73, 68, 32, 6, 1, 12, 45, 79, 72, 33, 6, 1, 13, 57, 124, 151, 105, 39, 6, 1, 14, 63, 138, 167, 114, 41, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

For n >= 1, the alternating row sums equal 0.

LINKS

Table of n, a(n) for n=0..77.

Marcel K. Goh and Jonah Saks, Alternating-sum statistics for certain sets of integers, arXiv:2206.12535 [math.CO], 2022.

EXAMPLE

Triangle T(n,k) begins:

  n/k 0  1  2  3  4  5 6

  0   1

  1   1  1

  2   1  2  1

  3   1  3  3  1

  4   1  4  5  2

  5   1  5  9  7  2

  6   1  6 11  8  2

  7   1  7 17 19 10  2

  8   1  8 21 25 14  3

  9   1  9 27 37 24  6

  10  1 10 31 42 26  6

  11  1 11 41 73 68 32 6

  12  1 12 45 79 72 33 6

  ...

For n=8 and k=5 the T(8,5)=3 sets are {1,2,3,5,7}, {1,3,4,5,7}, and {1,3,5,7,8}.

CROSSREFS

Row sums give A084422.

Cf. A000720, A036234, A186974, A320436.

Sequence in context: A099573 A107430 A330885 * A255741 A132892 A174448

Adjacent sequences:  A355142 A355144 A355145 * A355147 A355149 A355150

KEYWORD

nonn,tabf

AUTHOR

Marcel K. Goh, Jun 27 2022

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 August 14 17:12 EDT 2022. Contains 356122 sequences. (Running on oeis4.)