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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, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1
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OFFSET
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1,1
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COMMENTS
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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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LINKS
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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:
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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MATHEMATICA
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T[n_, k_] := If[k == n || k == n-2, 1, 0];
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PROG
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(PARI) tabl(nn) = {t129686 = matrix(nn, nn, n, k, (k<=n)*((k==n) || (k==(n-2)))); for (n = 1, nn, for (k = 1, n, print1(t129686[n, k], ", "); ); ); } \\ Michel Marcus, Feb 12 2014
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CROSSREFS
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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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