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Search: id:A086095
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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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+0
1
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| 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
(list; graph; listen)
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OFFSET
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1,3
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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 (Deutsch)
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PROGRAM
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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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Cf. A071085.
Adjacent sequences: A086092 A086093 A086094 this_sequence A086096 A086097 A086098
Sequence in context: A100887 A073592 A077929 this_sequence A112334 A113469 A060137
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KEYWORD
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sign,more
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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 Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 23 2004
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 11 2007
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