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A118230 Column 3 of triangle A118229, starting with row 1 to include leading zeros. 1

%I #11 Oct 27 2018 06:18:53

%S 0,0,1,-1,0,0,-1,2,0,-1,1,-1,-2,1,1,0,2,-2,-1,0,0,1,1,-1,-4,2,1,1,0,0,

%T 1,0,2,-6,3,0,-6,7,1,-2,8,-8,-5,-5,-2,12,3,-7,-6,-9,1,18,6,-21,-9,-5,

%U 4,25,-1,1,2,-39,-1,35,0,3,3,-18,-22,37,5,-5,8,-48,9,45,-10,-4,5,-55,10,40,-17,-35,4,-2,-11,61,4,-13

%N Column 3 of triangle A118229, starting with row 1 to include leading zeros.

%F Sum_{k=1..n, gcd(n,k)=1} a(k) = 1 when n=4, 0 elsewhere.

%t M[n_] := M[n] = Inverse[Table[If[r >= c, If[GCD[r-c+1, c] == 1, 1, 0], 0], {r, 1, n}, {c, 1, n}]];

%t T[n_, k_] := If[n<k || k<0, 0, M[n][[n, k]]];

%t a[n_] := T[n, 3];

%t Array[a, 90] (* _Jean-François Alcover_, Oct 27 2018, from PARI *)

%o (PARI) {a(n)=(matrix(n+2,n+2,r,c,if(r>=c,if(gcd(r-c+1,c)==1,1,0)))^-1)[n,3]}

%Y Cf. A118229.

%K sign

%O 1,8

%A _Leroy Quet_, _Paul D. Hanna_, Apr 16 2006

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Last modified March 28 07:33 EDT 2024. Contains 371235 sequences. (Running on oeis4.)