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A140736
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Triangle read by rows, X^n * [1,0,0,0,...]; where X = a tridiagonal matrix with (1,0,1,0,1,...) in the main diagonal and (1,1,1,...) in the sub and subsubdiagonals.
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2
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1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 5, 4, 6, 3, 1, 1, 1, 7, 6, 15, 10, 10, 4, 1, 1, 1, 9, 8, 28, 21, 35, 20, 15, 5, 1, 1, 1, 11, 10, 45, 36, 84, 56, 70, 35, 21, 6, 1, 1, 1, 13, 12, 66, 55, 165, 120, 210, 126, 126, 56, 28, 7, 1
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OFFSET
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1,7
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COMMENTS
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Row sums = F(2n), where A001906 = (1, 3, 8, 21, 55,...). Example: Row 4 terms = (1, 1, 5, 4, 6, 3, 1), sum = 21 = F(8).
The presence of the terms in Pascal's triangle points to a combinatorial version.
A140737 = triangle with reversed terms by rows: - Gary W. Adamson, May 25 2008
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LINKS
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Table of n, a(n) for n=1..64.
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1, 1;
1, 1, 3, 2, 1;
1, 1, 5, 4, 6, 3, 1;
1, 1, 7, 6, 15, 10, 10, 4, 1;
1, 1, 9, 8, 28, 21, 35, 20, 15, 5, 1;
1, 1, 11, 20, 45, 36, 84, 56, 70, 35, 21, 6, 1;
1, 1, 13, 12, 66, 55, 165, 120, 210, 126, 126, 56, 28, 7, 1;
...
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CROSSREFS
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Cf. A001906.
Cf. A140737.
Sequence in context: A079948 A106689 A027082 * A140056 A083663 A085427
Adjacent sequences: A140733 A140734 A140735 * A140737 A140738 A140739
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson & Roger L. Bagula, May 25 2008
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STATUS
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approved
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