OFFSET
1,1
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..100
Arnold Knopfmacher, Toufik Mansour, Augustine Munagi, Helmut Prodinger, Smooth words and Chebyshev polynomials, arXiv:0809.0551v1 [math.CO], 2008.
FORMULA
a(n) = Sum_{ d | n } A215338(d). - Joerg Arndt, Aug 13 2012
a(n) = (1/n) * Sum_{d | n} totient(n/d) * A124700(n). - Andrew Howroyd, Mar 18 2017
EXAMPLE
All solutions for n=3:
..3....2....6....4....4....1....5....2....2....6....3....3....5....6....5....1
..3....3....6....4....4....1....5....2....2....7....4....3....6....6....5....2
..4....3....6....5....4....1....5....3....2....7....4....3....6....7....6....2
..
..4....7....1
..5....7....1
..5....7....2
MATHEMATICA
sn[n_, k_] := 1/n*Sum[ DivisorSum[n, EulerPhi[#]*(1 + 2*Cos[i*Pi/(k + 1)])^(n/#) &], {i, 1, k}]; Table[sn[n, 7], {n, 1, 34}] // FullSimplify (* Jean-François Alcover, Oct 31 2017, after Joerg Arndt *)
PROG
(PARI)
/* from the Knopfmacher et al. reference */
default(realprecision, 99); /* using floats */
sn(n, k)=1/n*sum(i=1, k, sumdiv(n, j, eulerphi(j)*(1+2*cos(i*Pi/(k+1)))^(n/j)));
vector(66, n, round(sn(n, 7)) )
/* Joerg Arndt, Aug 09 2012 */
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Mar 01 2012
STATUS
approved