|
|
A011796
|
|
Number of irreducible alternating Euler sums of depth 6 and weight 6+2n.
|
|
4
|
|
|
1, 3, 9, 20, 42, 75, 132, 212, 333, 497, 728, 1026, 1428, 1932, 2583, 3384, 4389, 5598, 7084, 8844, 10962, 13442, 16380, 19776, 23751, 28301, 33561, 39536, 46376, 54081, 62832, 72624, 83655, 95931, 109668, 124866, 141778, 160398
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
a(n-6) is the number of aperiodic necklaces (Lyndon words) with 6 black beads and n-6 white beads.
|
|
REFERENCES
|
J. M. Borwein, D. H. Bailey and R. Girgensohn, Experimentation in Mathematics, A K Peters, Ltd., Natick, MA, 2004. x+357 pp. See p. 147.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: x*(1+x+2*x^2+2*x^3+3*x^4+2*x^6+x^7)/((1-x)^2*(1-x^2)^2*(1-x^3)*(1-x^6)).
G.f.: (1/(1-x)^6-1/(1-x^2)^3-1/(1-x^3)^2+1/(1-x^6))/6. - Herbert Kociemba, Oct 23 2016
a(n) = T(n,6), array T as in A051168.
|
|
MAPLE
|
a:= n-> (Matrix([[42, 20, 9, 3, 1, 0$7, -1, -4, -9]]). Matrix(15, (i, j)-> if (i=j-1) then 1 elif j=1 then [2, 1, -3, -1, 1, 4, -3, -3, 4, 1, -1, -3, 1, 2, -1][i] else 0 fi)^(n-5))[1, 1]: seq(a(n), n=1..50); # Alois P. Heinz, Aug 04 2008
|
|
MATHEMATICA
|
a[n_] := Sum[Binomial[(n+6)/d, 6/d]*MoebiusMu[d], {d, Divisors[GCD[6, n+6]]}]/(n+6); Array[a, 40] (* Jean-François Alcover, Feb 02 2015 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|