|
| |
|
|
A071095
|
|
Number of ways to tile hexagon of edges n, n+1, n+1, n, n+1, n+1 with diamonds of side 1.
|
|
3
|
|
|
|
1, 6, 175, 24696, 16818516, 55197331332, 872299918503728, 66345156372852988800, 24277282058281388285162560, 42730166102274086598901662210000, 361690697335823816369045433734882109375, 14721491647169381835282394824891766183125000000, 2880942480871157389699990094736740229925045312500000000
(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
|
Seiichi Manyama, Table of n, a(n) for n = 0..53
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
|
a(n) = 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=n, b=c=n+1.
a(n) ~ exp(1/12) * 3^(9*n^2/2 + 6*n + 23/12) / (A * n^(1/12) * 2^(6*n^2 + 8*n + 11/4)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Apr 26 2015
a(n) = (-1)^floor(n/2)*det(M(n)) where M(n) is the n X n matrix with m(i,j) = binomial(2*n+i+j,i+j). - Benoit Cloitre, Oct 22 2022
|
|
|
MATHEMATICA
|
Table[Product[(i+j+k+2)/(i+j+k+1), {i, 0, n-1}, {j, 0, n}, {k, 0, n}], {n, 0, 15}] (* Vaclav Kotesovec, Apr 26 2015 *)
|
|
|
PROG
|
(PARI) a(n) = prod(i=0, n-1, prod(j=0, n, prod(k=0, n, (i+j+k+2)/(i+j+k+1)))) \\ Michel Marcus, May 20 2013
|
|
|
CROSSREFS
|
Cf. A008793, A103905.
Sequence in context: A233225 A055165 A318538 * A134632 A024277 A012177
Adjacent sequences: A071092 A071093 A071094 * A071096 A071097 A071098
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
N. J. A. Sloane, May 28 2002
|
|
|
STATUS
|
approved
|
| |
|
|
