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A129372
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Triangle read by rows: T(n,k) = 1 if k divides n and n/k is odd, T(n,k) = 0 otherwise.
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8
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1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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FORMULA
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Sum_{k=1..n} T(n, k) = A001227(n) (row sums).
Sum_{k=1..n} (-1)^(k-1)*T(n, k) = (-1)^(n-1)*A001227(n).
Sum_{k=1..floor((n+1)/2)} T(n-k+1, k) = A183063(n+1). (End)
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EXAMPLE
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First few rows of the triangle:
1;
0, 1;
1, 0, 1;
0, 0, 0, 1;
1, 0, 0, 0, 1;
0, 1, 0, 0, 0, 1;
1, 0, 0, 0, 0, 0, 1;
0, 0, 0, 0, 0, 0, 0, 1;
1, 0, 1, 0, 0, 0, 0, 0, 1;
...
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MATHEMATICA
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A129372[n_, k_]:= If[Mod[n, k]==0 && OddQ[n/k], 1, 0];
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PROG
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(Magma)
A129372:= func< n, k | (n mod k) eq 0 and (Floor(n/k) mod 2) eq 1 select 1 else 0 >;
(SageMath)
def A129372(n, k): return 1 if (n%k)==0 and ((n/k)%2)==1 else 0
flatten([[A129372(n, k) for k in range(1, n+1)] for n in range(1, 16)]) # G. C. Greubel, Feb 01 2024
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Name changed and terms a(56) and beyond from Andrew Howroyd, Aug 10 2018
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STATUS
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approved
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