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A054344 Number of ways of covering a 2n X 2n lattice with 2n^2 dominoes of which exactly 6 are horizontal (or vertical) dominoes. 3
9, 1064, 21656, 197484, 1143366, 4927524, 17240292, 51631617, 137044523, 330284988, 735542444, 1533609350, 3024043008, 5684167992, 10249533240, 17821214019, 30006185613, 49097892704, 78305096016 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 2..1000

M. E. Fisher, Statistical mechanics of dimers on a plane lattice, Physical Review, 124 (1961), 1664-1672.

P. W. Kasteleyn, The Statistics of Dimers on a Lattice, Physica, 27 (1961), 1209-1225.

Index entries for sequences related to dominoes

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

FORMULA

a(n) = (1/720)*n*(n+1)*(120*n^7-300*n^6-70*n^5+363*n^4+416*n^3-231*n^2-394*n-264).

G.f.: x^2*(x^9-10*x^8+45*x^7-36*x^6+3096*x^5+17256*x^4+27724*x^3+11421*x^2+974*x+9)/(x-1)^10. - Colin Barker, Jun 26 2012

EXAMPLE

a(3) = 1064 because we have 1064 ways to cover a 36 X 36 lattice with exactly 6 horizontal (or vertical) dominoes and exactly 12 vertical (or horizontal) dominoes.

MATHEMATICA

CoefficientList[Series[(x^9-10*x^8+45*x^7-36*x^6+3096*x^5 +17256*x^4 +27724*x^3+11421*x^2+974*x+9)/(x-1)^10, {x, 0, 30}], x] (* Vincenzo Librandi, Jun 26 2012 *)

CROSSREFS

Cf. A004003, A002414, A038758.

Sequence in context: A277829 A286396 A174636 * A048912 A036411 A075412

Adjacent sequences:  A054341 A054342 A054343 * A054345 A054346 A054347

KEYWORD

nonn,easy

AUTHOR

Yong Kong (ykong(AT)curagen.com), May 06 2000

STATUS

approved

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Last modified September 16 06:48 EDT 2019. Contains 327090 sequences. (Running on oeis4.)