OFFSET
0,2
COMMENTS
Dimensions of Lie algebra associated to Yang-Lee algebra in the A. Connes and M. Dubois-Violette paper. - Roger L. Bagula, May 25 2007
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Latham Boyle, Paul J. Steinhardt, Self-Similar One-Dimensional Quasilattices, arXiv preprint arXiv:1608.08220 [math-ph], 2016.
A. Connes and M. Dubois-Violette, Yang-Mills Algebra, arXiv:math/0206205 [math.QA], 2002.
N. J. A. Sloane, Transforms
FORMULA
Product_{n=1..inf} 1/(1-x^n)^a(n) = 1/((1-x^2)*(1-4*x+x^2)).
a(n) = (1/n) * Sum_{k|n} moebius(n/k) (t1^k + t2^k), where t1, t2 are the roots of x^2-4x+1.
a(n) ~ (2+sqrt(3))^n / n. - Vaclav Kotesovec, Sep 11 2014
MAPLE
with(numtheory): f:= proc(n) option remember; `if`(n<1, `if`(n=0, 1, 0), 4*(f(n-1)-f(n-3)) +f(n-4)) end: c:= proc(n) option remember; local j; n*f(n) -add(c(j)*f(n-j), j=1..n-1) end: a:= proc(n) option remember; local d; `if`(n=0, 1, add(mobius(n/d)*c(d), d=divisors(n))/n) end: seq(a(n), n=0..27); # Alois P. Heinz, Sep 09 2008
MATHEMATICA
f[n_] := f[n] = If[n < 1, If[n == 0, 1, 0], f[n-4] + 4*(f[n-1] - f[n-3])]; c[n_] := c[n] = n*f[n] - Sum[c[j]*f[n-j], {j, 1, n-1}]; a[n_] := a[n] = If[n == 0, 1, Sum[c[d]*MoebiusMu[n/d], {d, Divisors[n]}]/n]; Table[a[n], {n, 0, 27}] (* Jean-François Alcover, Mar 14 2014, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 15 2002
EXTENSIONS
Edited by N. J. A. Sloane, May 16 2008 at the suggestion of R. J. Mathar
STATUS
approved