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 A081611 Number of numbers <= n having no 2 in their ternary representation. 6
 1, 2, 2, 3, 4, 4, 4, 4, 4, 5, 6, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 11, 12, 12, 12, 12, 12, 13, 14, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is also the size of the subset of [1..n] when numbers are added greedily so as to not contain a 3-term arithmetic progression, i.e., according to A003278: a(n) = the largest k such that A003278(k) <= n. (Cf. A003002, the size of the optimal (largest) 3-free subset of [1..n].) - Shreevatsa R, Oct 19 2009 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..10000 FORMULA a(n) + A081610(n) = n+1. From Michael Somos, Aug 31 2006: (Start) G.f. A(x) satisfies A(x)=(1+x)*(1+x+x^2)*A(x^3). G.f.: (1/(1-x))*Product_{k>=0} (1+x^(3^k)). a(n) = a(n-1) + A039966(n). (End) MATHEMATICA CoefficientList[Series[Product[1+x^(3^k), {k, 0, 5}]/(1-x), {x, 0, 100}], x] (* G. C. Greubel, Mar 29 2019 *) PROG (PARI) {a(n)=local(A, m); if(n<0, 0, m=1; A=1+O(x); while(m<=n, m*=3; A=(1+x)*(1+x+x^2)*subst(A, x, x^3)); polcoeff(A, n))} /* Michael Somos, Aug 31 2006 */ (PARI) first(n)=my(s, t); vector(n, k, t=Set(digits(k, 3)); s+=t[#t]<2) \\ Charles R Greathouse IV, Sep 02 2015 (PARI) my(x='x+O('x^100)); Vec(prod(k=0, 5, 1+x^(3^k))/(1-x)) \\ G. C. Greubel, Mar 29 2019 (Haskell) a081611 n = a081611_list !! n a081611_list = scanl1 (+) a039966_list -- Reinhard Zumkeller, Jan 28 2012 (MAGMA) R:=PowerSeriesRing(Integers(), 100); Coefficients(R!( (&*[1+x^(3^k): k in [0..5]])/(1-x) )); // G. C. Greubel, Mar 29 2019 (Sage) (product(1+x^(3^k) for k in (0..5))/(1-x)).series(x, 100).coefficients(x, sparse=False) # G. C. Greubel, Mar 29 2019 CROSSREFS Cf. A003278, A007089, A039966, A081603, A081608, A061392, A081610. Sequence in context: A303997 A276646 A029130 * A326539 A297995 A081228 Adjacent sequences:  A081608 A081609 A081610 * A081612 A081613 A081614 KEYWORD nonn AUTHOR Reinhard Zumkeller, Mar 23 2003 STATUS approved

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Last modified April 12 16:22 EDT 2021. Contains 342925 sequences. (Running on oeis4.)