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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
Jessica Striker, The alternating sign matrix polytope, arXiv:0705.0998 [math.CO], 2007-2009.
FORMULA
a(n) = 4*((n-2)^2 + 1) for n >= 3.
From Harvey P. Dale, Mar 05 2012: (Start)
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
(PARI) a(n)=([0, 1, 0; 0, 0, 1; 1, -3, 3]^n*[20; 8; 4])[1, 1] \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
Cf. A005130 (number of vertices).
Sequence in context: A305129 A032633 A294437 * A007290 A049031 A364583
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, May 09 2007
EXTENSIONS
More terms from Harvey P. Dale, Mar 05 2012
Initial 3 terms and formulas corrected by Ludovic Schwob, Feb 14 2024
STATUS
approved

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Last modified March 18 22:34 EDT 2024. Contains 370951 sequences. (Running on oeis4.)