A128445 Number of facets of the Alternating Sign Matrix polytope ASM(n).

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

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

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) 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

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

Initial 3 terms and formulas corrected by Ludovic Schwob, Feb 14 2024

Status

approved