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A030114 Number of distributive lattices; also number of paths with n turns when light is reflected from 10 glass plates. 1
1, 10, 55, 385, 2530, 17017, 113641, 760804, 5089282, 34053437, 227837533, 1524414737, 10199443436, 68241935348, 456589252304, 3054922560820, 20439707165252, 136756870048981, 915005341022187, 6122067418010887, 40961191948244094, 274060890253820561 (list; graph; refs; listen; history; text; internal format)
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.

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

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]

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 A197357 A164951

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

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Last modified October 21 12:12 EDT 2019. Contains 328299 sequences. (Running on oeis4.)