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 A072279 Dimension of n-th graded section of a certain Lie algebra. 8
 1, 4, 6, 16, 45, 144, 440, 1440, 4680, 15600, 52344, 177840, 608160, 2095920, 7262640, 25300032, 88517520, 310927680, 1095923400, 3874804560, 13737892896, 48829153920, 173949483240, 620963048160, 2220904271040, 7956987570576, 28553731537320, 102617166646800 (list; graph; refs; listen; history; text; internal format)
 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 Inverse EULER transform of A072335 (with its initial 1 omitted). Cf. A072337. Sequence in context: A231998 A056421 A032295 * A038236 A223269 A264471 Adjacent sequences: A072276 A072277 A072278 * A072280 A072281 A072282 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

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Last modified March 1 13:16 EST 2024. Contains 370433 sequences. (Running on oeis4.)