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A131078
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Periodic sequence (1, 1, 1, 1, 0, 0, 0, 0).
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11
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1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1
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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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a(1) = a(2) = a(3) = a(4) = 1, a(5) = a(6) = a(7) = a(8) = 0; for n > 8, a(n) = a(n-8).
G.f.: x/((1-x)*(1+x^4)).
a(n) = a(n-1)-a(n-4)+a(n-5), n>5.
a(n) = (1+(-1)^((2*n+11-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))/8))/2. (End)
a(n) = binomial(n+3,4) mod 2
a(n) = floor((n+3)/4) - 2*floor((n+3)/8). (End)
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PROG
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(PARI) {m=105; for(n=1, m, print1((n-1)%8<4, ", "))}
(Magma) m:=105; [ [1, 1, 1, 1, 0, 0, 0, 0][ (n-1) mod 8 + 1 ]: n in [1..m] ];
(Magma) &cat[[1, 1, 1, 1, 0, 0, 0, 0]: n in [0..10]];
/* or */ [Floor((1+(-1)^((2*n+11-(-1)^n+2*(-1)^((2*n+5-(-1)^n)/4))/8))/2): n in [1..60]]; // Vincenzo Librandi, May 31 2015
(Python)
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CROSSREFS
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Period 2*k: repeat k ones followed by k zeros: A000035(n+1) (k=1), A133872(n) (k=2), A088911 (k=3), this sequence (k=4), and A112713(n-1) (k=5).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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