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A294672 Number of disjoint covering systems of cardinality n, up to equivalence under shift. 1
1, 1, 2, 4, 10, 26, 75, 226, 718, 2368, 8083, 28367 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A disjoint covering system is a system of n congruences x == a_i (mod m_i) such that every integer is a solution to exactly one of the congruences. This sequence counts them up to "shift"; that is, two systems are the same if we can turn one into another by subtracting a constant from x.

LINKS

Table of n, a(n) for n=1..12.

B. Novak and S. Znam, Disjoint Covering Systems, The American Mathematical Monthly, Vol. 81, No. 1 (1974), 42-45.

Wikipedia, Covering system

EXAMPLE

For n = 3 there are three disjoint covering systems:

(a) x == 0 (mod 3), x == 1 (mod 3), x == 2 (mod 3)

(b) x == 0 (mod 2), x == 1 (mod 4), x == 3 (mod 4)

(c) x == 1 (mod 2), x == 0 (mod 4), x == 2 (mod 4)

but (b) and (c) are equivalent under shift.

CROSSREFS

Sequence in context: A006123 A006251 A049401 * A239077 A148099 A007579

Adjacent sequences:  A294669 A294670 A294671 * A294673 A294674 A294675

KEYWORD

nonn,more

AUTHOR

Jeffrey Shallit, Nov 06 2017

STATUS

approved

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Last modified February 20 09:06 EST 2018. Contains 299384 sequences. (Running on oeis4.)