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A104582
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Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product of the lower triangular matrix (Fibonacci(i-j+1)) and of the lower triangular matrix all of whose entries are equal to 1 (for j <= i).
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1
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1, 2, 1, 4, 2, 1, 7, 4, 2, 1, 12, 7, 4, 2, 1, 20, 12, 7, 4, 2, 1, 33, 20, 12, 7, 4, 2, 1, 54, 33, 20, 12, 7, 4, 2, 1, 88, 54, 33, 20, 12, 7, 4, 2, 1, 143, 88, 54, 33, 20, 12, 7, 4, 2, 1, 232, 143, 88, 54, 33, 20, 12, 7, 4, 2, 1, 376, 232, 143, 88, 54, 33, 20, 12, 7, 4, 2, 1, 609, 376, 232
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OFFSET
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1,2
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LINKS
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FORMULA
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T(i, j) = Fibonacci(i-j+3) - 1 for 1 <= j <= i and 0 otherwise. - Emeric Deutsch, Mar 23 2005
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EXAMPLE
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The first few rows of the triangle are:
1;
2, 1;
4, 2, 1;
7, 4, 2, 1;
12, 7, 4, 2, 1;
...
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MAPLE
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with(combinat): for i from 1 to 13 do seq(fibonacci(i-j+3)-1, j=1..i) od; # yields sequence in triangular form # Emeric Deutsch, Mar 23 2005
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CROSSREFS
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Sum of row n = Fibonacci(n+4) - n - 3 (A001924). Columns (starting from the diagonal entries) are the Fibonacci numbers -1 (A000071).
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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