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!)
A330618 Triangle read by rows: T(n,k) is the number of n-bead necklaces using exactly k colors with no adjacent beads having the same color. 4
0, 0, 1, 0, 0, 2, 0, 1, 3, 6, 0, 0, 6, 24, 24, 0, 1, 11, 80, 180, 120, 0, 0, 18, 240, 960, 1440, 720, 0, 1, 33, 696, 4410, 11340, 12600, 5040, 0, 0, 58, 1960, 18760, 73920, 137760, 120960, 40320, 0, 1, 105, 5508, 76368, 433944, 1209600, 1753920, 1270080, 362880 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,6
COMMENTS
In the case of n = 1, the single bead is considered to be cyclically adjacent to itself giving T(1,1) = 0. If compatibility with A208535 is wanted then T(1,1) should be 1.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)
FORMULA
T(n,k) = Sum_{j=1..k} (-1)^(k-j)*binomial(k,j)*A208535(n,j) for n > 1.
T(n,n) = (n-1)! for n > 1.
EXAMPLE
Triangle begins:
0;
0, 1;
0, 0, 2;
0, 1, 3, 6;
0, 0, 6, 24, 24;
0, 1, 11, 80, 180, 120;
0, 0, 18, 240, 960, 1440, 720;
0, 1, 33, 696, 4410, 11340, 12600, 5040;
0, 0, 58, 1960, 18760, 73920, 137760, 120960, 40320;
...
PROG
(PARI) \\ here U(n, k) is A208535(n, k) for n > 1.
U(n, k)={sumdiv(n, d, eulerphi(n/d)*(k-1)^d)/n - if(n%2, k-1)}
T(n, k)={sum(j=1, k, (-1)^(k-j)*binomial(k, j)*U(n, j))}
CROSSREFS
Column 3 is A093367.
Row sums are A330620.
Sequence in context: A254281 A295682 A195772 * A062104 A257783 A226874
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Dec 20 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 26 02:39 EST 2024. Contains 370335 sequences. (Running on oeis4.)