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A204418 Periodic sequence 1,0,1,..., arranged in a triangle.

%I A204418 #43 Dec 02 2021 19:57:00
%S A204418 1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,
%T A204418 0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,
%U A204418 1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1
%N A204418 Periodic sequence 1,0,1,..., arranged in a triangle.
%C A204418 Binomial transform is A130781.
%C A204418 Row sums: 1, 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 9, ... = A004396(n+1) = A131737 (n+2) .
%C A204418 Diagonal sums: 1, 0, 2, 1, 1, 3, 3, 1, 5, 3, 2, 6, 5, 2, 8, 5, 3, 9, 7, 3, 11, 7, 4, 12, 9, 4, 14, 9, 5, 15, ..
%C A204418 Essentially the same as A141571 and A011655. - _R. J. Mathar_, Jan 16 2012
%C A204418 As sequence a(n) this is the characteristic sequence for the mod m reduced odd numbers (i.e., gcd(2*n+1,m)=1, n >= 0) for each modulus m from 3*A003586 = [3,6,9,12,18,24,27,36,48,...]. - _Wolfdieter Lang_, Feb 04 2012
%C A204418 Disregarding the triangle: a(A173732(n)) = 1. - _Reinhard Zumkeller_, Apr 29 2012
%D A204418 Michel Rigo, Formal Languages, Automata and Numeration Systems, 2 vols., Wiley, 2014. Mentions this sequence - see "List of Sequences" in Vol. 2.
%H A204418 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1).
%F A204418 If k==0 mod(3), T(n+k,k) = 1, 0, 1, 1, 0, 1, 1, 0, 1, ... (A204418)
%F A204418 If k==1 mod(3), T(n+k,k) = 1, 0, 0, 1, 0, 0, 1, 0, 0, ... (A079978)
%F A204418 If n==2 mod(3), T(n+k,k) = 1, 1, 1, 1, 1, 1, 1, 1, 1, ... (A000012)
%F A204418 a(A016777(n)) = 0.
%F A204418 G.f.:(1+x^2)/(1-x^3).
%F A204418 G.f.: U(0) where U(k)=  1 + x^2/(1 - x/(x + 1/U(k+1))); (continued fraction, 3-step). - _Sergei N. Gladkovskii_, Oct 17 2012
%e A204418 Triangle begins:
%e A204418   1;
%e A204418   0, 1;
%e A204418   1, 0, 1;
%e A204418   1, 0, 1, 1;
%e A204418   0, 1, 1, 0, 1;
%e A204418   1, 0, 1, 1, 0, 1;
%e A204418   1, 0, 1, 1, 0, 1, 1;
%e A204418   0, 1, 1, 0, 1, 1, 0, 1;
%e A204418   1, 0, 1, 1, 0, 1, 1, 0, 1;
%o A204418 (PARI) a(n)=n%3!=1 \\ _Charles R Greathouse IV_, Jul 13 2016
%Y A204418 Cf. A011655.
%K A204418 nonn,tabl,easy
%O A204418 0,1
%A A204418 _Philippe Deléham_, Jan 15 2012