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A174037
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Triangle T(n, k, q) = Sum_{j>=0} q^j * floor(binomial(n, k)/2^j) with q = 2, read by rows.
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3
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1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 12, 16, 12, 1, 1, 13, 36, 36, 13, 1, 1, 16, 49, 92, 49, 16, 1, 1, 17, 93, 197, 197, 93, 17, 1, 1, 32, 124, 304, 464, 304, 124, 32, 1, 1, 33, 204, 540, 768, 768, 540, 204, 33, 1, 1, 36, 237, 752, 1556, 1788, 1556, 752, 237, 36, 1
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refs;
listen;
history;
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OFFSET
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0,5
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LINKS
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FORMULA
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T(n, k, q) = Sum_{j>=0} q^j * floor(binomial(n, k)/2^j) with q = 2.
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EXAMPLE
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Triangle begins as:
1;
1, 1;
1, 4, 1;
1, 5, 5, 1;
1, 12, 16, 12, 1;
1, 13, 36, 36, 13, 1;
1, 16, 49, 92, 49, 16, 1;
1, 17, 93, 197, 197, 93, 17, 1;
1, 32, 124, 304, 464, 304, 124, 32, 1;
1, 33, 204, 540, 768, 768, 540, 204, 33, 1;
1, 36, 237, 752, 1556, 1788, 1556, 752, 237, 36, 1;
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MATHEMATICA
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T[n_, k_, q_]:= Sum[q^j*Floor[Binomial[n, k]/2^j], {j, 0, 2*n}];
Table[T[n, k, 2], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 16 2021 *)
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PROG
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(Magma)
T:= func< n, k, q | (&+[q^j*Floor(Binomial(n, k)/2^j): j in [0..2*n]]) >;
[T(n, k, 2): k in [0..n], n in [0..12]]; // G. C. Greubel, Apr 16 2021
(Sage)
def T(n, k, q): return sum(q^j*( binomial(n, k)//2^j ) for j in (0..2*n))
flatten([[T(n, k, 2) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Apr 16 2021
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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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