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Search: id:A104569
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| A104569 |
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Triangle read by rows: T(i,j) is the (i,j)-entry (1<=j<=i) of the product Q*R of the infinite lower triangular matrices Q = [1; 1,3; 1,3,1; 1 3,1,3;...] and R = [1; 1,1; 1,1,1; 1,1,1,1;...]. |
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+0
3
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| 1, 4, 3, 5, 4, 1, 8, 7, 4, 3, 9, 8, 5, 4, 1, 12, 11, 8, 7, 4, 3, 13, 12, 9, 8, 5, 4, 1, 16, 15, 12, 11, 8, 7, 4, 3, 17, 16, 13, 12, 9, 8, 5, 4, 1, 20, 19, 16, 15, 12, 11, 8, 7, 4, 3, 21, 20, 17, 16, 13, 12, 9, 8, 5, 4, 1, 24, 23, 20, 19, 16, 15, 12, 11, 8, 7, 4, 3, 25, 24, 21, 20, 17, 16, 13
(list; table; graph; listen)
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OFFSET
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1,2
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FORMULA
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For 1<=j<=i: T(i, j)=2(i-j+1) if i and j are of opposite parity; T(i, j)=2(i-j)+1 if both i and j are odd; T(i, j)=2(i-j)+3 if both i and j are even. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 23 2005
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EXAMPLE
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The first few rows of the triangle are:
1;
4, 3;
5, 4, 1;
8, 7, 4, 3;
9, 8, 5, 4, 1;
...
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MAPLE
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T:=proc(i, j) if j>i then 0 elif i+j mod 2 = 1 then 2*(i-j)+2 elif i mod 2 = 1 and j mod 2 = 1 then 2*(i-j)+1 elif i mod 2 = 0 and j mod 2 = 0 then 2*(i-j)+3 else fi end: for i from 1 to 13 do seq(T(i, j), j=1..i) od; # yields sequence in triangular form (Deutsch)
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CROSSREFS
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Cf. A074377, A104570, A035608.
Row sums yield A074377. Columns 1, 3, 5, ... (starting at the diagonal entry) yield A042948. Columns 2, 4, 6, ... (starting at the diagonal entry) yield A014601. The product R*Q yields A104570.
Adjacent sequences: A104566 A104567 A104568 this_sequence A104570 A104571 A104572
Sequence in context: A011206 A075128 A074091 this_sequence A093619 A134186 A024688
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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 Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 23 2005
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