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 A206739 G.f.: 1/(1 - x/(1 - x^4/(1 - x^9/(1 - x^16/(1 - x^25/(1 - x^36/(1 -...- x^(n^2)/(1 -...))))))), a continued fraction. 7
 1, 1, 1, 1, 1, 2, 3, 4, 5, 7, 10, 14, 19, 26, 37, 52, 72, 99, 138, 193, 269, 373, 518, 722, 1006, 1399, 1944, 2705, 3766, 5241, 7290, 10141, 14112, 19638, 27323, 38012, 52889, 73593, 102398, 142470, 198225, 275809, 383760, 533954, 742923, 1033685, 1438254 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Table of n, a(n) for n=0..46. FORMULA a(n) = sum(k=0..n, T(n,k)), where T(n, m)=sum(i=1..(n-m)/3, binomial(m, i)*T((n-m)/3,i)), T(n,n)=1. - Vladimir Kruchinin, Mar 21 2015 G.f.: A(x)=1/B(x), where B(x) is g.f. of A290975. - Seiichi Manyama, Aug 18 2017 a(n) ~ c * d^n, where d = 1.391377080590304271048017099353... and c = 0.3625537262803710555422183139... - Vaclav Kotesovec, Aug 24 2017 EXAMPLE G.f.: A(x) = 1 + x + x^2 + x^3 + x^4 + 2*x^5 + 3*x^6 + 4*x^7 + 5*x^8 +... MATHEMATICA nmax = 50; CoefficientList[Series[1/Fold[(1 - #2/#1) &, 1, Reverse[x^(Range[nmax + 1]^2)]], {x, 0, nmax}], x] (* Vaclav Kotesovec, Aug 24 2017 *) PROG (PARI) {a(n)=local(CF=1+x*O(x^n), M=sqrtint(n+1)); for(k=0, M, CF=1/(1-x^((M-k+1)^2)*CF)); polcoeff(CF, n, x)} for(n=0, 55, print1(a(n), ", ")) (PARI) N = 66; q = 'q + O('q^N); G(k) = if(k>N, 1, 1 - q^((k+1)^2) / G(k+1) ); gf = 1 / G(0); Vec(gf) \\ Joerg Arndt, Jul 06 2013 (Maxima) T(n, m):=if n=m then 1 else sum(binomial(m, i)*T((n-m)/3, i), i, 1, (n-m)/3); makelist(sum(T(n, k), k, 0, n), n, 0, 20); /* Vladimir Kruchinin, Mar 21 2015 */ CROSSREFS Cf. A206740, A290975. Sequence in context: A087221 A352041 A295072 * A107586 A206737 A275174 Adjacent sequences: A206736 A206737 A206738 * A206740 A206741 A206742 KEYWORD nonn AUTHOR Paul D. Hanna, Feb 12 2012 STATUS approved

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Last modified September 18 14:57 EDT 2024. Contains 376000 sequences. (Running on oeis4.)