login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A276550 Array read by antidiagonals: T(n,k) = number of primitive (period n) bracelets using a maximum of k different colored beads. 7
1, 2, 0, 3, 1, 0, 4, 3, 2, 0, 5, 6, 7, 3, 0, 6, 10, 16, 15, 6, 0, 7, 15, 30, 45, 36, 8, 0, 8, 21, 50, 105, 132, 79, 16, 0, 9, 28, 77, 210, 372, 404, 195, 24, 0, 10, 36, 112, 378, 882, 1460, 1296, 477, 42, 0, 11, 45, 156, 630, 1848, 4220, 5890, 4380, 1209, 69, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Turning over will not create a new bracelet.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1275

G. Melancon, C. Reutenauer, On a Class of Lyndon Words Extending Christoffel Words and Related to a Multidimensional Continued Fraction Algorithm, J. Int. Seq. 16 (2013) #13.9.7, Corollary 6.

F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc.

F. Ruskey, Necklaces, Lyndon words, De Bruijn sequences, etc. [Cached copy, with permission, pdf format only]

FORMULA

T(n, k) = Sum_{d|n} mu(n/d) * A081720(n,k) for k<=n.

EXAMPLE

Table starts

1  2   3    4     5      6      7       8 ...

0  1   3    6    10     15     21      28 ...

0  2   7   16    30     50     77     112 ...

0  3  15   45   105    210    378     630 ...

0  6  36  132   372    882   1848    3528 ...

0  8  79  404  1460   4220  10423   22904 ...

0 16 195 1296  5890  20640  60021  151840 ...

0 24 477 4380 25275 107100 364854 1057392 ...

...

MAPLE

A276550 := proc(l, n)

    local d;

    add(numtheory[mobius](d)*binomial(n-1+l/d, n-1), d=numtheory[divisors](l)) ;

end proc:

for l from 1 to 10 do

    for n from 1 to 10 do

        printf("%a, ", A276550(l, n)) ;

    end do:

    printf("\n") ;

end do: # R. J. Mathar, Jan 21 2018

CROSSREFS

Columns 2-6 are A001371, A032294, A032295, A032296, A056347.

Cf. A081720, A273891, A276543, A152176.

Sequence in context: A208544 A208535 A284856 * A294438 A074650 A284871

Adjacent sequences:  A276547 A276548 A276549 * A276551 A276552 A276553

KEYWORD

nonn,tabl,easy

AUTHOR

Andrew Howroyd, Apr 09 2017

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 February 20 14:58 EST 2019. Contains 320327 sequences. (Running on oeis4.)