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A086095
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Permanent of the n X n matrix M where M(i,i) = 0 and for i != j, M(i,j) = mu(|i-j|) where mu( ) is the moebius function.
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1
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1, 0, 1, -2, 1, 0, 4, 16, 16, -64, 1184, -4176, 11588, -45320, 60177, -107154, 596001, -2059576, 9159736, 8005616, 313722880, 1052525600, 9682854977, 55241475020, 489566327904, 4159594989264, 34384770630704, 347985635900764, 3590752406671641, 36608921259384368
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OFFSET
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0,4
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LINKS
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MAPLE
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with(linalg):with(numtheory):mu:=proc(n) if n=0 then 0 else mobius(n) fi end:a:=(i, j)->mu(abs(i-j)):seq(permanent(matrix(n, n, a)), n=1..19); # the Maple mobius command is not used since it assigns mobius(0)=-1 # Emeric Deutsch, Dec 23 2004
# second Maple program:
a:= n-> `if`(n=0, 1, LinearAlgebra[Permanent](Matrix(n, (i, j)
-> `if`(i=j, 0, numtheory[mobius](abs(i-j)))))):
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MATHEMATICA
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a[n_] := Permanent[Table[MoebiusMu[Abs[i - j]], {i, 1, n}, {j, 1, n}]]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 19}] (* Jean-François Alcover, Jan 07 2016 *)
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PROG
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(PARI) permRWN(a)=n=matsize(a)[1]; if(n==1, return(a[1, 1])); n1=n-1; sg=1; m=1; nc=0; in=vector(n); x=in; for(i=1, n, x[i]=a[i, n]-sum(j=1, n, a[i, j])/2); p=prod(i=1, n, x[i]); while(m, sg=-sg; j=1; if((nc%2)!=0, j++; while(in[j-1]==0, j++)); in[j]=1-in[j]; z=2*in[j]-1; nc+=z; m=nc!=in[n1]; for(i=1, n, x[i]+=z*a[i, j]); p+=sg*prod(i=1, n, x[i])); return(2*(2*(n%2)-1)*p)
mobius(n)=if(n!=0, moebius(n), 0)
for(n=1, 40, a=matrix(n, n, i, j, mobius(abs(i-j))); print1(permRWN(a)", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 11 2007
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 24 2003
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EXTENSIONS
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More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 11 2007
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STATUS
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approved
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