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Search: id:A104568
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| A104568 |
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Triangle of numbers that are 0 or 1 mod 3. |
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+0
2
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| 1, 3, 1, 4, 3, 1, 6, 4, 3, 1, 7, 6, 4, 3, 1, 9, 7, 6, 4, 3, 1, 10, 9, 7, 6, 4, 3, 1, 12, 10, 9, 7, 6, 4, 3, 1, 13, 12, 10, 9, 7, 6, 4, 3, 1, 15, 13, 12, 10, 9, 7, 6, 4, 3, 1, 16, 15, 13, 12, 10, 9, 7, 6, 4, 3, 1, 18, 16, 15, 13, 12, 10, 9, 7, 6, 4, 3, 1, 19, 18, 16, 15, 13, 12, 10, 9, 7, 6, 4, 3, 1
(list; table; graph; listen)
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OFFSET
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0,2
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COMMENT
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The matrix operations (J * R), (R * J) are commutative since J * R = R * J. Row sums = A006578: 1, 4, 8, 14, 21, 30, 40... Rows and columns of the triangle are all 0 or 1 mod 3 terms: A032766: 1, 3, 4, 6, 7, 9, 10, 12... A104567 row sums also = A006578: 1, 4, 8, 14... A006578(2n-1) = A001082(2n)
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FORMULA
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All columns (with offset); and all rows (starting from the right) are 0 or 1 mod 3 (A032766). Extract the triangle from the product J * R; J = [1; 2, 1; 1, 2, 1; 2, 1, 2, 1;...]; R = [1; 1, 1; 1, 1, 1;...] (infinite lower triangular matrices, with the rest zeros).
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EXAMPLE
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The first few rows are:
1
3, 1;
4, 3, 1;
6, 4, 3, 1;
7, 6, 4, 3, 1;
9, 7, 6, 4, 3, 1;
...
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MAPLE
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it:=array(1..1000): i:=1: for n from 1 to 1000 do if n mod 3 <> 2 then it[i]:=n; i:=i+1 fi: od: for j from 1 to 25 do for k from j to 1 by -1 do printf(`%d, `, it[k]) od: od: (Sellers)
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CROSSREFS
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Cf. A104567, A006578, A001082, A104566.
Sequence in context: A064883 A090844 A008314 this_sequence A030758 A104764 A152842
Adjacent sequences: A104565 A104566 A104567 this_sequence A104569 A104570 A104571
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 16 2005
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Apr 09 2005
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