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A059486
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3-enumeration of 2n+1 X 2n+1 vertically symmetric alternating-sign matrices.
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1
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1, 1, 5, 126, 16038, 10320453, 33590259846, 553104735325740, 46084184498427053436, 19430969437346561065941390, 41463730793298298041665385308325, 447814224393522724673729884056814834500, 24479424309393636290695101063892553945412075000
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OFFSET
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0,3
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LINKS
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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]
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MAPLE
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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); ) } [From Harry J. Smith, Jun 27 2009]
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PROG
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(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); ) } [From Harry J. Smith, Jun 27 2009]
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CROSSREFS
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Cf. A025748.
Sequence in context: A201839 A156956 A015476 * A071196 A157438 A142803
Adjacent sequences: A059483 A059484 A059485 * A059487 A059488 A059489
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Feb 04 2001
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STATUS
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approved
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