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1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 0, 0, 3, 0, 1, 0, 1, 0, 0, 5, 1, 0, 1, 0, 1, 0, 0, 7, 1, 1, 0, 1, 0, 3, 0, 0, 11, 1, 1, 1, 0, 2, 0, 5, 0, 0, 0, 17, 0, 1, 1, 1, 0, 3, 0, 7, 0, 0, 27, 1, 0, 1, 1, 2, 0, 5, 0, 11, 0, 0, 40
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OFFSET
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1,15
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COMMENTS
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Row sums = A052284 starting at n=1: (1, 1, 1, 2, 3, 5, 7, 11, 17,...). As a property of eigentriangles, sum of n-th row terms = rightmost term of next row.
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LINKS
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FORMULA
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Triangle read by rows, A157423 * (A052284 * 0^(n-k)). A157423 = an infinite lower triangular matrix with A005171 in every column. (A052284 * 0^(n-k)) = an infinite lower triangular matrix with A052284: (1, 1, 1, 1, 2, 3, 5, 7, 11, 17, 27,...) as the main diagonal and the rest zeros.
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EXAMPLE
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First few rows of the triangle =
1;
0, 1;
0, 0, 1;
1, 0, 0, 1;
0, 1, 0, 0, 2;
1, 0, 1, 0, 0, 3;
0, 1, 0, 1, 0, 0, 5;
1, 0, 1, 0, 2, 0, 0, 7;
1, 1, 0, 1, 0, 3, 0, 0, 11;
1, 1, 1, 0, 2, 0, 5,0, 0, 17;
0, 1, 1, 1, 0, 3, 0, 7, 0, 0, 27;
1, 0, 1, 1, 2, 0, 5, 0, 11, 0, 0, 40;
0, 1, 0, 1, 2, 3, 0, 7, 0, 17, 0, 0, 61;
1, 0, 1, 0, 2, 3, 5, 0, 11, 0, 27, 0, 0, 92;
...
Example: row 5 = (0, 1, 0, 0, 2) = termwise products of (0, 1, 0, 0, 1) and
(1, 1, 1, 1, 2); where (0, 1, 0, 0, 2) = row 5 of triangle A157423 and
(1, 1, 1, 1, 2) = the first 5 terms of A052284.
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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