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A098172
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Triangle T(n,k) with diagonals T(n,n-k) = binomial(n,3k).
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3
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1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 4, 1, 0, 0, 0, 0, 10, 1, 0, 0, 0, 0, 1, 20, 1, 0, 0, 0, 0, 0, 7, 35, 1, 0, 0, 0, 0, 0, 0, 28, 56, 1, 0, 0, 0, 0, 0, 0, 1, 84, 84, 1, 0, 0, 0, 0, 0, 0, 0, 10, 210, 120, 1, 0, 0, 0, 0, 0, 0, 0, 0, 55, 462, 165, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 220, 924, 220, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,14
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COMMENTS
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The matrix inverse starts
1;
0, 1;
0, 0, 1;
0, 0, -1, 1;
0, 0, 4, -4, 1;
0, 0, -40, 40, -10, 1;
0, 0, 796, -796, 199, -20, 1;
0, 0, -27580, 27580, -6895, 693, -35, 1;
... (End)
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LINKS
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FORMULA
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Triangle T(n, k) = binomial(n, 3(n-k)).
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EXAMPLE
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Rows begin
{1},
{0,1},
{0,0,1},
{0,0,1,1},
{0,0,0,4,1},
{0,0,0,0,10,1},
...
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MATHEMATICA
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Table[Binomial[n, 3(n-k)], {n, 0, 12}, {k, 0, n}]//Flatten (*G. C. Greubel,Mar 15 2019 *)
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PROG
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(PARI) {T(n, k) = binomial(n, 3*(n-k))}; \\G. C. Greubel,Mar 15 2019
(Magma) [[Binomial(n, 3*(n-k)): k in [0..n]]: n in [0..12]]; //G. C. Greubel,Mar 15 2019
(Sage) [[binomial(n, 3*(n-k)) for k in (0..n)] for n in (0..12)] #G. C. Greubel,Mar 15 2019
(GAP) Flat(List([0..12], n-> List([0..n], k-> Binomial(n, 3*(n-k)) ))); #G. C. Greubel,Mar 15 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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