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Search: id:A104566
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| A104566 |
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Triangle read by rows: T(i,j) is the (i,j)-entry (1<=j<=i) of the product H*R of the infinite lower triangular matrices H = [1; 1,2; 1,2,1; 1 2,1,2;...] and R = [1; 1,1; 1,1,1; 1,1,1,1;...]. |
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+0
3
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| 1, 3, 2, 4, 3, 1, 6, 5, 3, 2, 7, 6, 4, 3, 1, 9, 8, 6, 5, 3, 2, 10, 9, 7, 6, 4, 3, 1, 12, 11, 9, 8, 6, 5, 3, 2, 13, 12, 10, 9, 7, 6, 4, 3, 1, 15, 14, 12, 11, 9, 8, 6, 5, 3, 2, 16, 15, 13, 12, 10, 9, 7, 6, 4, 3, 1, 18, 17, 15, 14, 12, 11, 9, 8, 6, 5, 3, 2, 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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1,2
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FORMULA
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For 1<=j<=i: T(i, j)=3(i-j+1)/2 if i and j are of opposite parity; T(i, j)=3(i-j)/2+1 if both i and j are odd; T(i, j)=3(i-j)/2+2 if both i and j are even. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 24 2005
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EXAMPLE
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The first few rows are
1;
3, 2;
4, 3, 1;
6, 5, 3, 2;
...
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MAPLE
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T:=proc(i, j) if j>i then 0 elif i mod 2 = 1 and j mod 2 = 1 then 3*(i-j)/2+1 elif i mod 2 = 0 and j mod 2 = 0 then 3*(i-j)/2+2 elif i+j mod 2 = 1 then 3*(i-j+1)/2 else fi end: for i from 1 to 14 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. A001082, A006578.
Row sums yield A001082. Columns 1,3,5,... (starting at the diagonal entry) yield A032766. Columns 2,4,6,... (starting at the diagonal entry) yield A045506.
Row sums = 1, 5, 8, 16, 21... (generalized octagonal numbers, A001082). A006578(2n-1) = A001082(2n).
Sequence in context: A106288 A013633 A016559 this_sequence A143156 A101403 A025509
Adjacent sequences: A104563 A104564 A104565 this_sequence A104567 A104568 A104569
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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 15 2005
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 24 2005
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