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Search: id:A141430
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| 1, 1, 1, 2, 5, 7, 7, 2, 8, 7, 4, 2, 2, 7, 1, 2, 5, 7, 7, 2, 8, 7, 4, 2, 2, 7, 1, 2, 5, 7, 7, 2, 8, 7, 4, 2, 2, 7, 1, 2, 5, 7, 7, 2, 8, 7, 4, 2, 2, 7
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OFFSET
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0,4
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COMMENT
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After the initial 1,1, the sequence is periodic with period length 12.
This period is a shuffled version of the two period-6 sequences A070366 and A010697. The sequence contains only the digits 1, 2, 4, 5, 7 and 8 (those of A141425).
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FORMULA
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a(n) = A000111(n) mod 9 = A004099(n) mod 9.
a(n+12) = a(n), n>1.
a(n)+a(n+6) =9 = A010734(n), n>1.
a(n+11-p)-a(n+p)= 6 (p=0 or 5), 0 (p=1 or 4), -3 (p=2 or 3), any n>1.
a(n) = (1/132)*{9*(n mod 12) + 31*[(n + 1) mod 12] + 42*[(n + 2) mod 12] + 20*[(n + 3) mod 12] - 57*[(n + 4) mod 12] + 64*[(n + 5) mod 12] + 9*[(n + 6) mod 12] - 13*[(n + 7) mod 12] - 24*[(n + 8) mod 12] - 2*[(n + 9) mod 12] + 75*[(n + 10) mod 12] - 46*[(n + 11) mod 12]} - [C(2*n,n) mod 2] - 6*{C[(n + 1)^2,n + 3] mod 2} [From Paolo P. Lava (ppl(AT)spl.at), Aug 25 2008]
G.f.: (6x^8-5x^7+x^6+2x^5+3x^4+x^3+1) / ((1-x)(x^2+1)(x^4-x^2+1)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2008
a(n)=9/2 +(-1)^[n/2]*A010686(n)/2 -3*A014021(n), n>1. - R. J. Mathar, Dec 05 2008
a(n)=4.5 - 1.5*cos(Pi*n/6) + 1/2*3^(1/2)*sin(Pi*n/6) - 0.5*cos(Pi*n/2) - 2.5*sin(Pi*n/2) - 1.5*cos(5*Pi*n/6) - 1/2*3^(1/2)*sin(5*Pi*n/6) [From Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 12 2008]
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CROSSREFS
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Sequence in context: A066035 A167554 A078320 this_sequence A021392 A131688 A096624
Adjacent sequences: A141427 A141428 A141429 this_sequence A141431 A141432 A141433
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KEYWORD
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nonn
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Aug 06 2008
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EXTENSIONS
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Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2008
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