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A166454
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Triangle read by rows: T(n, k) = (1/2)*(A007318(n,k) - A047999(n,k)).
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5
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1, 1, 1, 2, 3, 2, 2, 5, 5, 2, 3, 7, 10, 7, 3, 3, 10, 17, 17, 10, 3, 4, 14, 28, 35, 28, 14, 4, 4, 18, 42, 63, 63, 42, 18, 4, 5, 22, 60, 105, 126, 105, 60, 22, 5, 5, 27, 82, 165, 231, 231, 165, 82, 27, 5, 6, 33, 110, 247, 396, 462, 396, 247, 110, 33, 6
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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2,4
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COMMENTS
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Row sums = A120739: (1, 2, 7, 14, 30, 60, 127, 254, ...).
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LINKS
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FORMULA
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EXAMPLE
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First few rows of the triangle:
1;
1, 1;
2, 3, 2;
2, 5, 5, 2;
3, 7, 10, 7, 3;
3, 10, 17, 17, 10, 3;
4, 14, 28, 35, 28, 14, 4;
4, 18, 42, 63, 63, 42, 18, 4;
5, 22, 60, 105, 126, 105, 60, 22, 5;
5, 27, 82, 165, 231, 231, 165, 82, 27, 5;
6, 33, 110, 247, 396, 462, 396, 247, 110, 33, 6;
...
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MAPLE
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seq(seq(floor(binomial(n, m)/2), m=1..n-1), n=2..12); # Muniru A Asiru, Apr 14 2019
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MATHEMATICA
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T[n_, m_] = Floor[Binomial[n, m]/2]; Table[T[n, m], {n, 2, 12}, {m, 1, n-1}]//Flatten (* Roger L. Bagula, Mar 07 2010*)
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PROG
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(Haskell) Following Bagula's formula
a166454 n k = a166454_tabl !! (n-2) !! (k-1)
a166454_row n = a166454_tabl !! (n-2)
a166454_tabl = map (map (flip div 2) . init . tail) $ drop 2 a007318_tabl
(GAP) Flat(List([2..12], n->List([1..n-1], m->Int(Binomial(n, m)/2)))); # Muniru A Asiru, Apr 14 2019
(PARI) {T(n, k) = binomial(n, k)\2 };
for(n=2, 12, for(k=1, n-1, print1(T(n, k), ", "))) \\ G. C. Greubel, Apr 16 2019
(Magma) [[Floor(Binomial(n, k)/2): k in [1..n-1]]: n in [2..12]]; // G. C. Greubel, Apr 16 2019
(Sage) [[floor(binomial(n, k)/2) for k in (1..n-1)] for n in (2..12)] # G. C. Greubel, Apr 16 2019
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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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