OFFSET
1,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..100
FORMULA
a(n) = A328669(n) + 1 for n > 1. - Andrew Howroyd, Nov 01 2019
EXAMPLE
The a(7) = 12 Lyndon compositions with adjacent parts coprime:
(7)
(16) (25) (34)
(115)
(1114) (1213) (1132) (1123)
(11113) (11212)
(111112)
MATHEMATICA
LyndonQ[q_]:=Array[OrderedQ[{q, RotateRight[q, #]}]&, Length[q]-1, 1, And]&&Array[RotateRight[q, #]&, Length[q], 1, UnsameQ];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], Or[Length[#]==1, LyndonQ[#]&&And@@CoprimeQ@@@Partition[#, 2, 1, 1]]&]], {n, 20}]
PROG
(PARI)
b(n, q, pred)={my(M=matrix(n, n)); for(k=1, n, M[k, k]=pred(q, k); for(i=1, k-1, M[i, k]=sum(j=1, k-i, if(pred(j, i), M[j, k-i], 0)))); M[q, ]}
seq(n)={my(v=sum(k=1, n, k*b(n, k, (i, j)->gcd(i, j)==1))); vector(n, n, (n > 1) + sumdiv(n, d, moebius(d)*v[n/d])/n)} \\ Andrew Howroyd, Nov 01 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 02 2018
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Sep 08 2018
STATUS
approved