The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 12 11:55 EDT 2021. Contains 343821 sequences. (Running on oeis4.)