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A059486 3-enumeration of 2n+1 X 2n+1 vertically symmetric alternating-sign matrices. 3
1, 1, 5, 126, 16038, 10320453, 33590259846, 553104735325740, 46084184498427053436, 19430969437346561065941390, 41463730793298298041665385308325, 447814224393522724673729884056814834500, 24479424309393636290695101063892553945412075000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Harry J. Smith, Table of n, a(n) for n = 0..53

J. Propp, The many faces of alternating-sign matrices.

G. Kuperberg, Symmetry classes of alternating-sign matrices under one roof, arXiv math.CO/0008184 [Th. 3, but the formula there is incorrect]

MAPLE

A059486 := proc(n) local i, j, t1; t1 := 3^(2*n^2)/2^(2*n^2 + n); for i to 2*n + 1 do for j to 2*n + 1 do if i mod 2 <> 0 and j mod 2 = 0 then t1 := t1*(3*j - 3*i + 1)/(3*j - 3*i) end if end do end do; t1 end proc;

e(n)= { local(A); A=Vec((1 - (1 - 9*x + O(x^(2*n + 1)))^(1/3))/(3*x)); matdet(matrix(n, n, i, j, A[i+j]))/3^n; } { for (n = 0, 100, a=e(n); if (a > 10^(10^3 - 6), break); write("b059486.txt", n, " ", a); ) } # Harry J. Smith, Jun 27 2009

MATHEMATICA

a[n_] := Module[{i, j, t1}, t1 = 3^(2*n^2)/2^(2*n^2 + n); For[i = 1, i <= 2*n + 1, i++, For[j = 1, j <= 2*n + 1, j++, If[Mod[i, 2] != 0 && Mod[j, 2] == 0, t1 = t1*(3*j - 3*i + 1)/(3*j - 3*i)]]]; t1];

Table[a[n], {n, 0, 12}] (* Jean-Fran├žois Alcover, Nov 23 2017, translated from Maple *)

PROG

(PARI) a(n)=local(A); if(n<0, 0, A=Vec((1-(1-9*x+O(x^(2*n+1)))^(1/3))/(3*x)); matdet(matrix(n, n, i, j, A[i+j]))/3^n)

(PARI) e(n)= { local(A); A=Vec((1 - (1 - 9*x + O(x^(2*n + 1)))^(1/3))/(3*x)); matdet(matrix(n, n, i, j, A[i+j]))/3^n; } { for (n = 0, 100, a=e(n); if (a > 10^(10^3 - 6), break); write("b059486.txt", n, " ", a); ) } \\ Harry J. Smith, Jun 27 2009

CROSSREFS

Cf. A025748.

Sequence in context: A278080 A156956 A015476 * A071196 A115233 A157438

Adjacent sequences:  A059483 A059484 A059485 * A059487 A059488 A059489

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 04 2001

STATUS

approved

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Last modified January 17 05:26 EST 2019. Contains 319207 sequences. (Running on oeis4.)