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A197916
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Related to the periodic sequence A171654.
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0
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0, 1, 6, 7, 2, 3, 8, 9, 4, 5, 10, 11, 6, 7, 12, 13, 8, 9, 14, 15, 10, 11, 16, 17, 12, 13, 18, 19, 14, 15, 20, 21, 16, 17, 22, 23, 18, 19, 24, 25, 20, 21, 26, 27, 22, 23, 28, 29, 24, 25, 30, 31, 26, 27, 32, 33, 28, 29, 34, 35, 30, 31, 36, 37, 32, 33, 38, 39
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OFFSET
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0,3
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COMMENTS
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All numbers appear twice except numbers 0,1,2,3,4,5 which appear once. - From A. Salagnad, Oct 19 2011.
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LINKS
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FORMULA
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a(n)=Sum_k>=0 {A030308(n,k)*b(k)} with b(0)=1, b(1)=6 and b(k)=2^(k-1) for k>1.
G.f. ( -x*(-1-5*x-x^2+5*x^3) ) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 20 2011
a(n) = n/2+(11-(-1)^n)/4 -5*A057077(n)/2. - R. J. Mathar, Oct 20 2011
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MATHEMATICA
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LinearRecurrence[{1, 0, 0, 1, -1}, {0, 1, 6, 7, 2}, 80] (* Harvey P. Dale, Jul 30 2019 *)
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PROG
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(PARI) a(n)=([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; -1, 1, 0, 0, 1]^n*[0; 1; 6; 7; 2])[1, 1] \\ Charles R Greathouse IV, Jul 06 2017
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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