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Search: id:A129686
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| A129686 |
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Triangle read by rows: row n is 0^(n-3), 1, 0, 1. |
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10
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| 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Alternate term operator, sums.
Let A129686 = matrix M, with V any sequence as a vector. Then M*V is the alternate term sum operator. Given V = [1,2,3,...], M*V = [1, 2, 4, 6, 8, 10, 12, 14,...]. The analogous operation using A097807, (the pairwise operator), gives [1, 3, 5, 7, 9, 11, 13, 15,..]. Binomial transform of A129686 = A124725. A129686 * A007318 = A129687. Row sums of A129686 = (1, 1, 2, 2, 2,...).
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FORMULA
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As an infinite lower triangular matrix, (1,1,1,...) in the main diagonal, (0,0,0,...) in the subdiagonal and (1,1,1,...) in the subsubdiagonal; with the rest zeros. (1, 0, 1, 0, 0, 0,...) in every column.
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EXAMPLE
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First few rows of the triangle are:
1;
0, 1;
1, 0, 1;
0, 1, 0, 1
0, 0, 1, 0, 1;
0, 0, 0, 1, 0, 1;
...
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CROSSREFS
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Cf. A124725, A129687.
Sequence in context: A129372 A004539 A023960 this_sequence A104974 A024711 A128174
Adjacent sequences: A129683 A129684 A129685 this_sequence A129687 A129688 A129689
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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), Apr 28 2007
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