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Search: id:A113655
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| A113655 |
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Invert blocks of three in the sequence of natural numbers. |
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+0
3
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| 3, 2, 1, 6, 5, 4, 9, 8, 7, 12, 11, 10, 15, 14, 13, 18, 17, 16, 21, 20, 19, 24, 23, 22, 27, 26, 25, 30, 29, 28, 33, 32, 31, 36, 35, 34, 39, 38, 37, 42, 41, 40, 45, 44, 43, 48, 47, 46, 51, 50, 49, 54, 53, 52, 57, 56, 55, 60, 59, 58, 63, 62, 61, 66, 65, 64, 69, 68, 67, 72, 71, 70
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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a(n)=3*floor((n+2)/3) - (n-1) mod 3. - Robert G. Wilson v (rgwv(at)rgwv.com) and Zak Seidov (zakseidov(AT)yahoo.com), Jan 20 2006
a(n)=a(n-3)+3=a(n-1)+a(n-3)-a(n-4) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Dec 02 2008]
G.f.: (3*x-x^2-x^3+2*x^4)/(1-x-x^3+x^4) = x*(3-x-x^2+2*x^3)/((1+x+x^2)*(1-x)^2) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 25 2009]
a(n)=1+1/3*(-1/2-(1/2*I)*sqrt(3))^(-2)*(-1/2-(1/2*I)*sqrt(3))^n+1/3*(-1/2+(1/2*I) *sqrt(3))^(-2)*(-1/2+(1/2*I)*sqrt(3))^n+n-(1/6*I)*sqrt(3)*(-1/2+(1/2*I) *sqrt(3))^n+3/2*(-1/2-(1/2*I)*sqrt(3))^n+3/2*(-1/2+(1/2*I)*sqrt(3))^n+(1/6*I) *sqrt(3)*(-1/2-(1/2*I)*sqrt(3))^n+2/3*(-1/2-(1/2*I)*sqrt(3))^(-1)*(-1/2-(1/2*I) *sqrt(3))^n+2/3*(-1/2+(1/2*I)*sqrt(3))^(-1)*(-1/2+(1/2*I)*sqrt(3))^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Mar 31 2009]
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MATHEMATICA
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f[n_] := Switch[ Mod[n, 3], 0, n - 2, 1, n + 2, 2, n]; Array[f, 72] (* Robert G. Wilson v *)
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PROGRAM
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(PARI) a(n)=2+n-2*((n+2)%3) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 25 2009]
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CROSSREFS
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Sequence in context: A120771 A115094 A165958 this_sequence A114155 A079513 A139624
Adjacent sequences: A113652 A113653 A113654 this_sequence A113656 A113657 A113658
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KEYWORD
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nonn
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AUTHOR
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Parag D. Mehta (pmehta23(AT)gmail.com), Jan 16 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 18 2006
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