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1, 1, 1, 1, 5, 1, 1, 7, 7, 1, 1, 11, 13, 11, 1, 1, 13, 27, 27, 13, 1, 1, 17, 39, 65, 39, 17, 1, 1, 19, 61, 111, 111, 61, 19, 1, 1, 23, 79, 193, 221, 193, 79, 23, 1, 1, 25, 109, 283, 433, 433, 283, 109, 25, 1, 1, 29, 133, 425, 715, 925, 715, 425, 133, 29, 1
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table;
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OFFSET
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0,5
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COMMENTS
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Row sums = A131405: (1, 2, 7, 16, 37, 82, 179, ...).
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LINKS
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FORMULA
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T(n,k) = 4*binomial(n, k) + 1 - 2*binomial(floor(n + k)/2), k) - 2*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, 5, 1;
1, 7, 7, 1;
1, 11, 13, 11, 1;
1, 13, 27, 27, 13, 1;
1, 17, 39, 65, 39, 17, 1;
...
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PROG
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(PARI) T(n, k) = if(k <= n, 4*binomial(n, k) + 1 - 2*binomial((n + k)\2, k) - 2*binomial(n-(k+1)\2, k\2), 0) \\ Andrew Howroyd, Aug 09 2018
(Magma) /* As triangle */ [[4*Binomial(n, k) + 1 - 2*Binomial(Floor(n + k) div 2, k) - 2*Binomial(n-Floor((k+1)/2), Floor(k/2)): k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Aug 10 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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STATUS
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approved
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