login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A327396 Triangle read by rows: T(n,k) is the number of n-bead necklace structures with beads of exactly k colors and no adjacent beads having the same color. 7
0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 3, 5, 2, 1, 0, 0, 3, 10, 8, 2, 1, 0, 1, 7, 33, 40, 18, 3, 1, 0, 0, 11, 83, 157, 104, 28, 3, 1, 0, 1, 19, 237, 650, 615, 246, 46, 4, 1, 0, 0, 31, 640, 2522, 3318, 1857, 495, 65, 4, 1, 0, 1, 63, 1817, 9888, 17594, 13311, 4911, 944, 97, 5, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,18

COMMENTS

Permuting the colors does not change the necklace structure.

Equivalently, the number of k-block partitions of an n-set up to rotations where no block contains cyclically adjacent elements of the n-set.

LINKS

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

EXAMPLE

Triangle begins:

  0;

  0, 1;

  0, 0,  1;

  0, 1,  1,    1;

  0, 0,  1,    1,    1;

  0, 1,  3,    5,    2,     1;

  0, 0,  3,   10,    8,     2,     1;

  0, 1,  7,   33,   40,    18,     3,    1;

  0, 0, 11,   83,  157,   104,    28,    3,   1;

  0, 1, 19,  237,  650,   615,   246,   46,   4,  1;

  0, 0, 31,  640, 2522,  3318,  1857,  495,  65,  4, 1;

  0, 1, 63, 1817, 9888, 17594, 13311, 4911, 944, 97, 5, 1;

  ...

PROG

(PARI)

R(n) = {Mat(Col([Vecrev(p/y, n) | p<-Vec(intformal(sum(m=1, n, eulerphi(m) * subst(serlaplace((y-1)*exp(-x + O(x*x^(n\m))) - y + exp(-x + sumdiv(m, d, y^d*(exp(d*x + O(x*x^(n\m)))-1)/d)) ), x, x^m))/x), -n)]))}

{ my(A=R(12)); for(n=1, #A, print(A[n, 1..n])) } \\ Andrew Howroyd, Oct 09 2019

CROSSREFS

Columns k=3..4 are A327397, A328130.

Partial row sums include A306888, A309673.

Row sums are A328150.

Cf. A152175, A261139, A208535.

Sequence in context: A327693 A240752 A342277 * A021288 A140735 A183206

Adjacent sequences:  A327393 A327394 A327395 * A327397 A327398 A327399

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Oct 04 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 00:11 EDT 2021. Contains 348204 sequences. (Running on oeis4.)