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A216953
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Triangle read by rows: T(n,k) (n>=1, 1<=k<=n) = number of binary sequences of length n with minimal period k.
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2
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2, 2, 2, 2, 0, 6, 2, 2, 0, 12, 2, 0, 0, 0, 30, 2, 2, 6, 0, 0, 54, 2, 0, 0, 0, 0, 0, 126, 2, 2, 0, 12, 0, 0, 0, 240, 2, 0, 6, 0, 0, 0, 0, 0, 504, 2, 2, 0, 0, 30, 0, 0, 0, 0, 990, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2046, 2, 2, 6, 12, 0, 54, 0, 0, 0, 0, 0, 4020, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8190, 2, 2, 0, 0, 0, 0, 126, 0, 0, 0, 0, 0, 0, 16254
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OFFSET
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1,1
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REFERENCES
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LINKS
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FORMULA
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If k divides n, T(n,k) = A027375(k), otherwise 0.
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EXAMPLE
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Triangle begins:
2,
2, 2,
2, 0, 6,
2, 2, 0, 12,
2, 0, 0, 0, 30,
2, 2, 6, 0, 0, 54,
2, 0, 0, 0, 0, 0, 126,
2, 2, 0, 12, 0, 0, 0, 240,
2, 0, 6, 0, 0, 0, 0, 0, 504,
2, 2, 0, 0, 30, 0, 0, 0, 0, 990,
...
For n=4 the 16 sequences are:
0000, 1111, period 1,
0101, 1010, period 2,
and the rest have period 4.
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MAPLE
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with(numtheory): A027375:=n->add( mobius(d)*2^(n/d), d in divisors(n));
if n mod k = 0 then A027375(k) else 0; fi; end;
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MATHEMATICA
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a027375[n_] := DivisorSum[n, MoebiusMu[n/#]*2^#&];
T[n_, k_] := If[Divisible[n, k], a027375[k], 0];
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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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