A030115 Number of distributive lattices; also number of paths with n turns when light is reflected from 11 glass plates.

1, 11, 66, 506, 3641, 26818, 196119, 1437799, 10532302, 77173602, 565424068, 4142793511, 30353430420, 222394369223, 1629443428021, 11938642758854, 87472304803355, 640893994357062, 4695716053827835, 34404674660198306

Offset

0,2

Comments

Let M(11) be the 11 X 11 matrix (0,0,0,1)/(0,0,1,1)/(0,1,1,1)/(1,1,1,1) and let v(11) be the vector (1,1,1,1,1,1,1,1,1); then v(11)*M(11)^n = (x,y,z,t,u,v, w,m,n,o,a(n)) - Benoit Cloitre, Sep 29 2002

References

J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124.

J. Haubrich, Multinacci Rijen [Multinacci sequences], Euclides (Netherlands), Vol. 74, Issue 4, 1998, pp. 131-133.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124. [Annotated scanned copy]

G. Kreweras, Les préordres totaux compatibles avec un ordre partiel, Math. Sci. Humaines No. 53 (1976), 5-30.

Index entries for linear recurrences with constant coefficients, signature (6,15,-35,-35,56,28,-36,-9,10,1,-1).

Formula

G.f.: -(x -1)*(x^3 -x^2 -2*x +1)*(x^6 +x^5 -6*x^4 -6*x^3 +8*x^2 +8*x +1)/(x^11 -x^10 -10*x^9 +9*x^8 +36*x^7 -28*x^6 -56*x^5 +35*x^4 +35*x^3 -15*x^2 -6*x +1). [Colin Barker, Nov 09 2012]

Mathematica

CoefficientList[Series[-(x - 1) (x^3 - x^2 - 2 x + 1) (x^6 + x^5 - 6 x^4 - 6 x^3 + 8 x^2 + 8 x + 1)/(x^11 -x^10 - 10 x^9 + 9 x^8 + 36 x^7 - 28 x^6 - 56 x^5 + 35 x^4 + 35 x^3 - 15 x^2 - 6 x + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 19 2013 *)

Prog

(PARI) k=11; M(k)=matrix(k, k, i, j, if(1-sign(i+j-k), 0, 1)); v(k)=vector(k, i, 1); a(n)=vecmax(v(k)*M(k)^n)

Crossrefs

See also A006356-A006359, A025030, A030112-A030116.

Sequence in context: A256583 A210392 A316110 * A091929 A345036 A244304

Adjacent sequences: A030112 A030113 A030114 * A030116 A030117 A030118

Keyword

nonn,easy

Author

Jacques Haubrich (jhaubrich(AT)freeler.nl)

Extensions

More terms from Benoit Cloitre, Sep 29 2002

Status

approved