A232974 Number of irreducible packed words of length n.

1, 2, 2, 10, 66, 538, 5170, 56906, 704226, 9671930, 145992338, 2403271594, 42869336130, 824103252058, 16991417367538, 374154425946890, 8765990409737634, 217771226025864122, 5718895163944768850, 158315176568802482794, 4608155971186431515394

Offset

0,2

Comments

a(7) had a typo in the arXiv link on page 10 in Table 3 of i_n.

Links

Table of n, a(n) for n=0..20.

G. H. E. Duchamp, N. Hoang-Nghia, A. Tanasa, A word Hopf algebra based on the selection/quotient principle, Séminaire Lotharingien de Combinatoire 68 (2013), Article B68c.

G. H. E. Duchamp, N. Hoang-Nghia, A. Tanasa, A word Hopf algebra based on the selection/quotient principle, arXiv:1207.6522 [math.CO], 2012-2013.

Formula

G.f.: 2 - (1 - 2*x / (1 - 1*x / (1 - 4*x / (1 - 2*x / (1 - 6*x ...))))) = 2 - 1 / f(x) where f() is the g.f. for A000629. - Michael Somos, Mar 05 2014

INVERT transform of a(1..) = [2, 2, 10, 66, 538, 5170, 56906, ...] is A000629(1..) = [2, 6, 26, 150, 1082, 9366, 94586, ...]. - Michael Somos, Mar 06 2014

Example

G.f. = 1 + 2*x + 2*x^2 + 10*x^3 + 66*x^4 + 538*x^5 + 5170*x^6 + 56906*x^7 + ...
The packed irreducible words for n=1 are 0, 1; for n=2 are 11, 21; for n=3 are 101, 111, 121, 201, 211, 212, 221, 231, 312, 321. - Michael Somos, Mar 05 2014

Mathematica

nmax = 21;
A629[x_] = Sum[PolyLog[-n, 1/2] x^n, {n, 0, nmax}];
CoefficientList[2 - 1/A629[x] + O[x]^nmax, x] (* Jean-François Alcover, Aug 17 2018, after Michael Somos *)

Crossrefs

Cf. A000629.

Sequence in context: A059494 A052647 A326983 * A181334 A032034 A002250

Adjacent sequences: A232971 A232972 A232973 * A232975 A232976 A232977

Keyword

nonn

Author

N. J. A. Sloane, Dec 06 2013

Extensions

a(11)-a(20) from Michael Somos, Mar 05 2014

Status

approved