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A143158
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Triangle read by rows, T(n,k) = Sum_{j=k..n} mu(j).
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2
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1, 0, -1, -1, -2, -1, -1, -2, -1, 0, -2, -3, -2, -1, -1, -1, -2, -1, 0, 0, 1, -2, -3, -2, -1, -1, 0, -1, -2, -3, -2, -1, -1, 0, -1, 0, -2, -3, -2, -1, -1, 0, -1, 0, 0, -1, -2, -1, 0, 0, 1, 0, 1, 1, 1, -2, -3, -2, -1, -1, 0, -1, 0, 0, 0, -1, -2, -3, -2, -1, -1, 0, -1, 0, 0, 0, -1, 0, -3, -4, -3, -2, -2, -1, -2, -1, -1, -1, -2, -1, -1, -2, -3, -2, -1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,5
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COMMENTS
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LINKS
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FORMULA
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Triangle read by rows, T(n,k) = Sum_{j=k..n} mu(j), where mu(n) = A008683.
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EXAMPLE
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First few rows of the triangle =
1;
0, -1;
-1, -2, -1;
-1, -2, -1, 0;
-2, -3, -2, -1, -1;
-2, -3, -2, -1, -1, 0, -1;
-2, -3, -2, -1, -1, 0, -1, 0;
-1, -2, -1, 0, 0, 1, 0, 1, 1, 1;
...
For example, T(5,3) = (-2) = Sum(-1, 0, -1), since mu(n) = 1, -1, -1, 0, -1, ...
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MATHEMATICA
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Table[Sum[MoebiusMu@ j, {j, k, n}], {n, 14}, {k, n}] // Flatten (* Michael De Vlieger, Dec 17 2015 *)
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PROG
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(Haskell)
import Data.List (tails)
a143158 n k = a143158_tabl !! (n-1) !! (k-1)
a143158_row n = a143158_tabl !! (n-1)
a143158_tabl = map (map sum . init . tails) a054527_tabl
(PARI) T(n, k) = sum(j=k, n, moebius(j))
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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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