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

1,4

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,...]).

Links

Table of n, a(n) for n=1..105.

Example

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; ...

Prog

(PARI) {T(n, k)=if(n<k, 0, prod(i=0, n, matrix(n, n, r, c, if(r>=c, if((r+i)%(c+i)==0, 1, 0))))[n, k])}

Crossrefs

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

Sequence in context: A158948 A140224 A075993 * A117466 A136266 A292047

Adjacent sequences: A117167 A117168 A117169 * A117171 A117172 A117173

Keyword

nonn,tabl

Author

Wouter Meeussen and Paul D. Hanna, Mar 05 2006

Status

approved