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1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 6, 7, 6, 1, 1, 7, 14, 14, 7, 1, 1, 9, 20, 33, 20, 9, 1, 1, 10, 31, 56, 56, 31, 10, 1, 1, 12, 40, 97, 111, 97, 40, 12, 1, 1, 13, 55, 142, 217, 217, 142, 55, 13, 1, 1, 15, 67, 213, 358, 463, 358, 213, 67, 15, 1, 1, 16, 86, 287, 590, 841, 841, 590, 287, 86, 16, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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Row sums = A131403: (1, 2, 5, 10, 21, 44, 93, ...).
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LINKS
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FORMULA
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T(n,k) = 2*binomial(n, k) + 1 - binomial(floor(n + k)/2), k) - binomial(n-floor((k+1)/2), floor(k/2)). - Andrew Howroyd, Aug 09 2018
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1;
1, 3, 1;
1, 4, 4, 1;
1, 6, 7, 6, 1;
1, 7, 14, 14, 7, 1;
1, 9, 20, 33, 20, 9, 1;
1, 10, 31, 56, 56, 31, 10, 1;
...
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PROG
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(PARI) T(n, k) = if(k <= n, 2*binomial(n, k) + 1 - binomial((n + k)\2, k) - binomial(n-(k+1)\2, k\2), 0) \\ Andrew Howroyd, Aug 09 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Missing terms inserted and a(55) and beyond from Andrew Howroyd, Aug 09 2018
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STATUS
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approved
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