A117170 Triangle of coefficients for the Inverse Shift-Moebius transform, read by rows.

1, 1, 1, 2, 0, 1, 2, 1, 0, 1, 3, 1, 0, 0, 1, 3, 2, 1, 0, 0, 1, 4, 1, 1, 0, 0, 0, 1, 3, 3, 1, 1, 0, 0, 0, 1, 6, 1, 2, 1, 0, 0, 0, 0, 1, 5, 4, 1, 1, 1, 0, 0, 0, 0, 1, 5, 2, 2, 1, 1, 0, 0, 0, 0, 0, 1, 6, 4, 2, 2, 1, 1, 0, 0, 0, 0, 0, 1, 7, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 7, 6, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1

Offset: 1

Author

Wouter Meeussen and Paul D. Hanna, Mar 05 2006

Keywords

• nonn
• tabl

Comments

Column k = Inverse-Shift-Moebius transform of all zeros except for a single '1' in position k: [0,0,0,..(k-1)zeros..,1,0,0,0,...].

Column 1 is A117171 and equals Inverse-Shift-Moebius([1,0,0,0,...]).

Column 2 is A117172 and equals Inverse-Shift-Moebius([0,1,0,0,...]).

Column 3 is A117173 and equals Inverse-Shift-Moebius([0,0,1,0,...]).

Row sums give A117174 and equals Inverse-Shift-Moebius([1,1,1,...]).

Examples

			Triangle begins:
1;
1, 1;
2, 0, 1;
2, 1, 0, 1;
3, 1, 0, 0, 1;
3, 2, 1, 0, 0, 1;
4, 1, 1, 0, 0, 0, 1;
3, 3, 1, 1, 0, 0, 0, 1;
6, 1, 2, 1, 0, 0, 0, 0, 1;
5, 4, 1, 1, 1, 0, 0, 0, 0, 1;
5, 2, 2, 1, 1, 0, 0, 0, 0, 0, 1;
6, 4, 2, 2, 1, 1, 0, 0, 0, 0, 0, 1;
7, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1;
7, 6, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1;
10, 3, 4, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1;
7, 6, 2, 3, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1; ...
		

Crossrefs

Cf. A117171 (column 1), A117172 (column 2), A117173 (column 3), A117174 (row sums), A117165 (inverse), A117162, A008683; A117176.

Programs

PARI

{T(n,k)=if(n=c,if((r+i)%(c+i)==0,1,0))))[n,k])}