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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A071094 Number of ways to tile hexagon of edges n, n, n+1, n, n, n+1 with diamonds of side 1. 1
1, 3, 50, 4116, 1646568, 3184461423, 29706808370096, 1335119245893326400, 288882990167192721013376, 300792059519113653077154558000, 1506680146887473588202049621593937500, 36298820709557430183399305000196605531250000, 4205446372314569673006362329181090368935937500000000, 2342761095072644391194625697884219372917666852341417500000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

J. Propp, Enumeration of matchings: problems and progress, pp. 255-291 in L. J. Billera et al., eds, New Perspectives in Algebraic Combinatorics, Cambridge, 1999 (see page 261).

LINKS

Table of n, a(n) for n=0..13.

J. Propp, Updated article

J. Propp, Enumeration of matchings: problems and progress, in L. J. Billera et al. (eds.), New Perspectives in Algebraic Combinatorics

FORMULA

Product_{i=0..a-1} Product_{j=0..b-1} Product_{k=0..c-1} (i+j+k+2)/(i+j+k+1) with a=b=n, c=n+1.

a(n)=Product{k=0..n, C(2n+k,n+k)/C(n+k,k)}; - Paul Barry, May 13 2008

a(n) ~ exp(1/12) * 3^(9*n^2/2 + 3*n + 5/12) / (A * n^(1/12) * 2^(6*n^2 + 4*n + 3/4)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Apr 26 2015

MATHEMATICA

Table[Product[(i+j+k+2)/(i+j+k+1), {i, 0, n-1}, {j, 0, n-1}, {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Apr 26 2015 *)

PROG

(PARI) a(n) = prod(k=0, n, binomial(2*n+k, n+k)/binomial(n+k, k)) \\ Michel Marcus, May 20 2013

CROSSREFS

Sequence in context: A217767 A185157 A078674 * A144987 A304055 A305449

Adjacent sequences:  A071091 A071092 A071093 * A071095 A071096 A071097

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 28 2002

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 29 18:30 EDT 2020. Contains 338067 sequences. (Running on oeis4.)