Search: id:A113655
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%I A113655
%S A113655 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,
%T A113655 25,30,29,28,33,32,31,36,35,34,39,38,37,42,41,40,45,44,43,48,47,46,51,
%U A113655 50,49,54,53,52,57,56,55,60,59,58,63,62,61,66,65,64,69,68,67,72,71,70
%N A113655 Invert blocks of three in the sequence of natural numbers.
%F A113655 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
%F A113655 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]
%F A113655 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]
%F A113655 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]
%t A113655 f[n_] := Switch[ Mod[n, 3], 0, n - 2, 1, n + 2, 2, n]; Array[f, 72] (* 
               Robert G. Wilson v *)
%o A113655 (PARI) a(n)=2+n-2*((n+2)%3) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 
               Mar 25 2009]
%Y A113655 Sequence in context: A120771 A115094 A165958 this_sequence A114155 A079513 
               A139624
%Y A113655 Adjacent sequences: A113652 A113653 A113654 this_sequence A113656 A113657 
               A113658
%K A113655 nonn
%O A113655 1,1
%A A113655 Parag D. Mehta (pmehta23(AT)gmail.com), Jan 16 2006
%E A113655 More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jan 18 2006

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