A293375 Triangle read by rows: T(n, k), for 1 <= k <= n, where T(n, k) is defined in A192763.

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

Offset: 1

Author

Michael Somos, Oct 07 2017

Keywords

• sign
• tabl

Comments

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.

Examples

			Triangle begins:
1;
2, -2;
1,  2, -3;
1, -2,  1,  0;
0,  2,  2,  1, -5;
1, -2, -3, -2,  0, 6;
...
		

Links

• M. Granvik, Is this a recurrence for the Mertens function plus 2?, Math StackExchange question 50719.

Crossrefs

Cf. A192763.

Programs

Mathematica

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}]];

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)))};