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Search: id:A117170
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| A117170 |
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Triangle of coefficients for the Inverse Shift-Moebius transform, read by rows. |
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+0
8
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| 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; listen)
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OFFSET
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1,4
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COMMENT
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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,...]).
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EXAMPLE
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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; ...
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PROGRAM
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(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])}
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CROSSREFS
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Cf. A117171 (column 1), A117172 (column 2), A117173 (column 3), A117174 (row sums), A117165 (inverse), A117162, A008683; A117176.
Sequence in context: A091064 A140224 A075993 this_sequence A117466 A136266 A054523
Adjacent sequences: A117167 A117168 A117169 this_sequence A117171 A117172 A117173
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KEYWORD
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nonn,tabl
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AUTHOR
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Wouter Meeussen (wouter.meeussen(AT)pandora.be) and Paul D. Hanna (pauldhanna(AT)juno.com), Mar 05 2006
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