OFFSET
1,8
COMMENTS
Turning over will not create a new bracelet. Permuting the colors of the beads will not change the structure.
REFERENCES
M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275
FORMULA
T(n, k) = Sum_{d|n} mu(n/d) * A152176(d, k).
EXAMPLE
Triangle starts:
1
0 1
0 1 1
0 2 2 1
0 3 5 2 1
0 5 13 11 3 1
0 8 31 33 16 3 1
0 14 80 136 85 27 4 1
0 21 201 478 434 171 37 4 1
0 39 533 1849 2270 1249 338 54 5 1
...
PROG
Ach(n)={my(M=matrix(n, n, i, k, i>=k)); for(i=3, n, for(k=2, n, M[i, k]=k*M[i-2, k] + M[i-2, k-1] + if(k>2, M[i-2, k-2]))); M}
R(n)={Mat(Col([Vecrev(p/y, n) | p<-Vec(intformal(sum(m=1, n, eulerphi(m) * subst(serlaplace(-1 + exp(sumdiv(m, d, y^d*(exp(d*x + O(x*x^(n\m)))-1)/d))), x, x^m))/x))]))}
T(n)={my(M=(R(n)+Ach(n))/2); Mat(vectorv(n, n, sumdiv(n, d, moebius(d)*M[n/d, ])))}
{ my(A=T(12)); for(n=1, #A, print(A[n, 1..n])) } \\ Andrew Howroyd, Sep 20 2019
CROSSREFS
Row sums are A276548.
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Apr 09 2017
STATUS
approved