|
|
A128445
|
|
Number of facets of the Alternating Sign Matrix polytope ASM(n).
|
|
3
|
|
|
1, 1, 2, 8, 20, 40, 68, 104, 148, 200, 260, 328, 404, 488, 580, 680, 788, 904, 1028, 1160, 1300, 1448, 1604, 1768, 1940, 2120, 2308, 2504, 2708, 2920, 3140, 3368, 3604, 3848, 4100, 4360, 4628, 4904, 5188, 5480, 5780, 6088, 6404, 6728, 7060, 7400, 7748, 8104
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
The number of vertices (Bressoud) is Product_{j=0..n-1}(3j+1)!/(n+j)!.
|
|
REFERENCES
|
D. M. Bressoud, Proofs and confirmations: the story of the alternating sign matrix conjecture, MAA Spectrum, 1999.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 4*((n-2)^2 + 1) for n >= 3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n > 5.
G.f.: (2*x^5+x^4+4*x^3+2*x^2-4*x+1)/(1-x)^3. (End)
|
|
MATHEMATICA
|
Table[4((n-2)^2+1), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {20, 8, 4}, 50] (* Harvey P. Dale, Mar 05 2012 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|