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A004197
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Triangle read by rows. T(n, k) = n - k if n - k < k, otherwise k.
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14
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0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0, 0, 1, 2
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,13
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COMMENTS
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Table of min(x,y), where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),...
Triangle T(n,k) read by rows: T(n,k) = min(k,n-k). - Philippe Deléham, Feb 25 2014
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LINKS
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FORMULA
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2^T(n,k) = A144464(n,k), 3^T(n,k) = A152714(n,k), 4^T(n,k) = A152716(n,k), 5^T(n,k) = A152717(n,k). - Philippe Deléham, Feb 25 2014
a(n) = (1/2)*(t - 1 - abs(t^2 - 2*n - 1)), where t = floor(sqrt(2*n+1)+1/2). - Ridouane Oudra, May 03 2019
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EXAMPLE
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Top left corner of table:
0 0 0 0
0 1 1 1
0 1 2 2
0 1 2 3
Triangle T(n,k) begins:
0;
0, 0;
0, 1, 0;
0, 1, 1, 0;
0, 1, 2, 1, 0;
0, 1, 2, 2, 1, 0;
0, 1, 2, 3, 2, 1, 0;
0, 1, 2, 3, 3, 2, 1, 0;
0, 1, 2, 3, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 5, 6, 5, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 5, 6, 6, 5, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 5, 6, 7, 6, 5, 4, 3, 2, 1, 0;
0, 1, 2, 3, 4, 5, 6, 7, 7, 6, 5, 4, 3, 2, 1, 0;
... (End)
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MAPLE
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T := (n, k) -> if n - k < k then n - k else k fi:
for n from 0 to 9 do seq(T(n, k), k=0..n) od; # Peter Luschny, May 07 2023
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MATHEMATICA
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Flatten[Table[IntegerExponent[2^(n - k) 3^k, 6], {n, 0, 20}, {k, 0, n}]] (* Fred Daniel Kline, May 29 2012 *)
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PROG
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(Haskell)
a004197 n k = a004197_tabl !! n !! k
a004197_tabl = map a004197_row [0..]
a004197_row n = hs ++ drop (1 - n `mod` 2) (reverse hs)
where hs = [0..n `div` 2]
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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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