This site is supported by donations to The OEIS Foundation.

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A181119 Transpose-complementary plane partitions. 3
 1, 2, 84, 81796, 1844536720, 962310111888300, 11608208114358751650000, 3236574482779383546336417240000, 20853456581643133066208521560263633137920, 3104385823530881109001458753652585998600603921849920, 10676554307318599842868990948461304923921623250562199975300214736 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The complement of a plane partition inside an m*m*m cube consists of the boxes which are within the cube, but not in the plane partition, rotated in an appropriate way. a(n) is the number of plane partitions inside an 2n*2n*2n cube whose (matrix) transpose when written as an 2n*2n array is the same as its complement. LINKS R. P. Stanley, Symmetries of Plane Partitions, J. Comb. Theory Ser. A 43 (1986), 103-113. P. J. Taylor, Counting distinct dimer hex tilings, Preprint, 2015. Wikipedia, Plane partition FORMULA a(n) = binomial(3n-1,n)*Product(i=1..2n-2,Product(j=i..2n-2,(2n+i+j+1)/(i+j+1))). a(n) ~ exp(1/24) * 3^(9*n^2 - 3*n/2 - 1/24) / (sqrt(A) * n^(1/24) * 2^(12*n^2 - n - 1/3)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Feb 28 2015 EXAMPLE When n=2, there are two transpose-complementary plane partitions, [1 1] and [2 1], both of whose transpose and complement is equal to themselves. [1 1]     [1 0] MATHEMATICA Table[Binomial[3n-1, n]Product[(2n+i+j+1)/(i+j+1), {i, 1, 2n-2}, {j, i, 2n-2}], {n, 0, 10}] (* Harvey P. Dale, Jan 27 2012 *) PROG (PARI) a(n) = binomial(3*n-1, n)*prod(i=1, 2*n-2, prod(j=i, 2*n-2, (2*n+i+j+1)/(i+j+1))); \\ Michel Marcus, Jun 18 2015 CROSSREFS Cf. A008793, A051255, A078920, A123352. Sequence in context: A215263 A265591 A157063 * A157315 A244947 A078166 Adjacent sequences:  A181116 A181117 A181118 * A181120 A181121 A181122 KEYWORD nonn,nice AUTHOR Arvind Ayyer, Jan 21 2011 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 10 17:19 EST 2016. Contains 279005 sequences.