A030114 Number of distributive lattices; also number of paths with n turns when light is reflected from 10 glass plates.

1, 10, 55, 385, 2530, 17017, 113641, 760804, 5089282, 34053437, 227837533, 1524414737, 10199443436, 68241935348, 456589252304, 3054922560820, 20439707165252, 136756870048981, 915005341022187, 6122067418010887, 40961191948244094, 274060890253820561

Offset

0,2

Comments

Let M(10) be the 10 X 10 matrix (0,0,0,1)/(0,0,1,1)/(0,1,1,1)/(1,1,1,1) and let v(10) be the vector (1,1,1,1,1,1,1,1,1); then v(10)*M(10)^n = (x,y,z,t,u,v, w,m,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 (5,15,-20,-35,21,28,-8,-9,1,1).

Formula

G.f.: 1/(-x-1/(-x-1/(-x-1/(-x-1/(-x-1/(-x-1/(-x-1/(-x-1/(-x-1/(-x-1)))))))))) = -(x^9 +x^8 -8*x^7 -7*x^6 +21*x^5 +15*x^4 -20*x^3 -10*x^2 +5*x +1)/((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)). [Colin Barker, Nov 09 2012]

Mathematica

CoefficientList[Series[-(x^9 + x^8 - 8 x^7 - 7 x^6 + 21 x^5 + 15 x^4 - 20 x^3 - 10 x^2 + 5 x + 1)/((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, 0, 40}], x] (* Vincenzo Librandi, Oct 19 2013 *)

Prog

(PARI) k=10; 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: A199413 A054629 A290359 * A001557 A367938 A197357

Adjacent sequences: A030111 A030112 A030113 * A030115 A030116 A030117

Keyword

nonn,easy

Author

Jacques Haubrich (jhaubrich(AT)freeler.nl)

Extensions

More terms from Benoit Cloitre, Sep 29 2002

a(20)-a(21) from Vincenzo Librandi, Oct 19 2013

Status

approved