A293375 - OEIS

%I #15 Oct 07 2017 21:57:34

%S 1,2,-2,1,2,-3,1,-2,1,0,0,2,2,1,-5,1,-2,-3,-2,0,6,0,2,1,1,2,1,-7,0,-2,

%T 2,0,2,-2,0,0,0,2,-3,1,1,-3,2,0,0,1,-2,1,-2,-5,-2,1,-2,0,10,0,2,2,1,0,

%U 0,1,2,2,1,-11,0,-2,-3,0,2,6,2,0,-3,-2,0,0,-1

%N Triangle read by rows: T(n, k), for 1 <= k <= n, where T(n, k) is defined in A192763.

%C The function T(n, k) = T(k, n) is defined for k > n also but only the values for 1 <= k <= n as a triangular array are listed here.

%H M. Granvik, <a href="http://math.stackexchange.com/questions/50719/">Is this a recurrence for the Mertens function plus 2?</a>, Math StackExchange question 50719.

%e Triangle begins:

%e 1;

%e 2, -2;

%e 1,  2, -3;

%e 1, -2,  1,  0;

%e 0,  2,  2,  1, -5;

%e 1, -2, -3, -2,  0, 6;

%e ...

%t T[ n_, k_] := Which[ n < 1 || k < 1, 0, k > n, T[ k, n], k == 1, If[ n < 3, n, (n T[ n - 1, 1] - Sum[ T[ n, i], {i, 2, n - 1}]) / (n + 1)], n > k , T[ k, Mod[ n, k, 1]], True, - Sum[ T[ n, i], {i, n - 1}]];

%o (PARI) {T(n, k) = if( n<1 || k<1, 0, k>n, T(k, n), k==1, if( n<3, n, (n * T(n-1, 1) - sum( i=2, n-1, T(n, i))) / (n+1)), n>k, T(k, (n-1)%k+1), -sum( i=1, n-1, T(n, i)))};

%Y Cf. A192763.

%K sign,tabl

%O 1,2

%A _Michael Somos_, Oct 07 2017