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 A291148 Expansion of 1 - x/(1 - x^2/(1 - x^3/(1 - x^4/(1 - x^5/(1 - x^6/(1 - ... - x^n/(1 - ...))))))), a continued fraction. 8
 1, -1, 0, -1, 0, -1, -1, -1, -2, -2, -4, -4, -7, -9, -13, -19, -25, -38, -51, -75, -104, -149, -211, -298, -426, -600, -857, -1211, -1724, -2444, -3471, -4930, -6995, -9940, -14104, -20038, -28444, -40397, -57362, -81453, -115675, -164250, -233262, -331227 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS The sequence b(n>=1) = 1, 0, 1, 0, 1, 1, 1, 2, 2, 4, 4, 7, ... of absolute values counts fountains of n coins that cannot be separated into two or more fountains by cutting vertically through the fountain without splitting a coin. (This separation requires that the fountain is a left-right sequence of more elementary fountains counted by b(n).) A005169(n) = Sum_{compositions n=n1+n2+n3+...} Product b(n1)*b(n2)*.... - R. J. Mathar, Aug 22 2018 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..1000 FORMULA Convolution inverse of A005169. a(n) ~ c * d^n, where d = 1.42009048763893649946106129818306075366296460727614... and c = -0.093433697175825717154301151812109730023054876584907211486145769... - Vaclav Kotesovec, Oct 16 2017 EXAMPLE G.f. = 1 - x - x^3 - x^5 - x^6 - x^7 - 2*x^8 - 2*x^9 - ... CROSSREFS Cf. A005169, A290975, A291147. Sequence in context: A034396 A364193 A253412 * A032190 A222737 A005852 Adjacent sequences: A291145 A291146 A291147 * A291149 A291150 A291151 KEYWORD sign AUTHOR Seiichi Manyama, Aug 18 2017 STATUS approved

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Last modified August 9 02:18 EDT 2024. Contains 375024 sequences. (Running on oeis4.)