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A128445 Number of facets of the Alternating Sign Matrix polytope ASM(n). 3
20, 8, 4, 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

0,1

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

Table of n, a(n) for n=0..47.

Jessica Striker, The alternating sign matrix polytope, arXiv:0705.0998 [math.CO], 2007-2009.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 4*((n-2)^2 + 1).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), n > 2. - Harvey P. Dale, Mar 05 2012

G.f.: -4*(5 - 13*x + 10*x^2)/(x-1)^3.  - Harvey P. Dale, Mar 05 2012

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

Sequence in context: A196102 A196099 A102409 * A097395 A108967 A097390

Adjacent sequences:  A128442 A128443 A128444 * A128446 A128447 A128448

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, May 09 2007

EXTENSIONS

More terms from Harvey P. Dale, Mar 05 2012

STATUS

approved

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Last modified January 17 10:21 EST 2019. Contains 319218 sequences. (Running on oeis4.)