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 A086095 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..36 MAPLE 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)))))): seq(a(n), n=0..18); # Alois P. Heinz, Jan 28 2021 MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A008683, A071085. Sequence in context: A178039 A185411 A254882 * A322119 A363731 A112334 Adjacent sequences: A086092 A086093 A086094 * A086096 A086097 A086098 KEYWORD sign AUTHOR Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 24 2003 EXTENSIONS More terms from Emeric Deutsch, Dec 23 2004 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 11 2007 a(0) and a(26)-a(29) from Pontus von Brömssen, Jan 28 2021 STATUS approved

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Last modified April 25 10:22 EDT 2024. Contains 371967 sequences. (Running on oeis4.)