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A104974
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A Fredholm-Rueppel triangle.
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2
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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, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Riordan array ( (Sum_{k>=0} x^(2^k)/x^2) - 1/x, x).
Diagonal sums are A070939(n+1), with interpolated zeros.
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LINKS
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FORMULA
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Sum_{k=0..n} T(n, k) = A000523(n+1).
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EXAMPLE
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Triangle begins as:
1;
0, 1;
1, 0, 1;
0, 1, 0, 1;
0, 0, 1, 0, 1;
0, 0, 0, 1, 0, 1;
1, 0, 0, 0, 1, 0, 1;
0, 1, 0, 0, 0, 1, 0, 1;
0, 0, 1, 0, 0, 0, 1, 0, 1;
0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1;
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MAPLE
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end proc:
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MATHEMATICA
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Table[Mod[CatalanNumber[n-k+1], 2], {n, 0, 15}, {k, 0, n}]//Flatten (* G. C. Greubel, Jun 08 2021 *)
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PROG
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(Magma) [(Catalan(n-k+1) mod 2): k in [0..n], n in [0..15]]; // G. C. Greubel, Jun 08 2021
(Sage) flatten([[mod(catalan_number(n-k+1), 2) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, Jun 08 2021
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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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