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A171398 `X(n,k)' triangle read by rows. X(n,k) is the number of k-subsets of Z_n up to (u,z)-equivalence. 0
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 3, 3, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 4, 6, 4, 3, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,13

COMMENTS

Let Z_n={0,1,...,n-1} denote the integers mod n,

let U(n) denote the units mod n, the elements in Z_n relatively prime to n.

Let S and S' be two k-subsets of Z_n.

Define an equivalence relation on the set of k-subsets as follows:

S is (u,z)-equivalent to S' iff there is a u in U(n) and a z in Z_n such that S=uS'+z.

Then define X(n,k) to be the number of such (u,z)-equivalence classes.

This sequence is the `X(n,k)' triangle read by rows.

The triangle begins

1

1,1

1,1,1

1,1,1,1

1,1,2,1,1

1,1,1,1,1,1

1,1,3,3,3,1,1

1,1,1,2,2,1,1,1

1,1,3,4,6,4,3,1,1

For example row 8 is 1,1,3,4,6,4,3,1,1.

We have X(8,3)=4 because there are 4 (u,z)-equivalence classes of 3-subsets in Z_8,

their representatives are: {0,1,2}, {0,1,3}, {0,1,4}, and {0,2,4}.

REFERENCES

The row sums of the `X(n,k)' triangle give sequence A002729.

LINKS

Table of n, a(n) for n=1..45.

CROSSREFS

Sequence in context: A161606 A300362 A248145 * A113607 A082586 A160094

Adjacent sequences:  A171395 A171396 A171397 * A171399 A171400 A171401

KEYWORD

nonn,tabl

AUTHOR

John P. McSorley, Dec 07 2009

STATUS

approved

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Last modified July 5 03:37 EDT 2020. Contains 335459 sequences. (Running on oeis4.)