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A039658
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Related to enumeration of edge-rooted catafusenes.
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7
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0, 1, 2, 5, 8, 18, 28, 64, 100, 237, 374, 917, 1460, 3679, 5898, 15183, 24468, 64055, 103642, 275011, 446380, 1197616, 1948852, 5277070, 8605288, 23483743, 38362198, 105392983, 172423768, 476459938, 780496108, 2167743688, 3554991268
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OFFSET
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1,3
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COMMENTS
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This sequence appears in Table I, p. 533, in Cyvin et al. (1992) and Table I, p. 1174, in Cyvin et al. (1994).
In Cyvin et al. (1992), it is defined through eq. (22), p. 535. We have a(n) = Sum_{i=1..n-1} M(i)*M(n-i), where M(2*n) = M(2*n-1) = A007317(n) for n >= 1.
In Cyvin et al. (1992), it is used in the calculation of sequence A026118. See eq. (34), p. 536, in Cyvin et al. (1992).
(The word "annelated" in the title of Cyvin et al. (1994) is spelled "annealated" in the text of Cyvin et al. (1992).)
(End)
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LINKS
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Eric Weisstein's World of Mathematics, Fusenes.
Eric Weisstein's World of Mathematics, Polyhex.
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FORMULA
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G.f.: (1+x)*(1 - 3*x^2 - sqrt(1 - 6*x^2 + 5*x^4))/(2*x^2*(1-x)) (eq. (9), p. 1175, in Cyvin et al. (1994)).
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MATHEMATICA
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Rest[CoefficientList[Series[(1+x) (1-3x^2-Sqrt[1-6x^2+5x^4])/(2x^2 (1-x)), {x, 0, 40}], x]] (* Harvey P. Dale, Oct 30 2016 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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