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A117170 Triangle of coefficients for the Inverse Shift-Moebius transform, read by rows. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 24 00:33 EDT 2021. Contains 348217 sequences. (Running on oeis4.)