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A039658 Related to enumeration of edge-rooted catafusenes. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

From Petros Hadjicostas, Jan 13 2019: (Start)

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)

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

S. J. Cyvin, Zhang Fuji, B. N. Cyvin, Guo Xiaofeng, and J. Brunvoll, Enumeration and classification of benzenoid systems. 32. Normal perifusenes with two internal vertices, J. Chem. Inform. Comput. Sci., 32 (1992), 532-540.

S. J. Cyvin, B. N. Cyvin, J. Brunvoll, and E. Brendsdal, Enumeration and classification of certain polygonal systems representing polycyclic conjugated hydrocarbons: annelated catafusenes, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180.

Eric Weisstein's World of Mathematics, Fusenes.

Eric Weisstein's World of Mathematics, Polyhex.

FORMULA

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)).

For n >= 1, a(n) = Sum_{i=1..n-1} A007317(floor((i+1)/2)) * A007317(floor((n-i+1)/2)). - Petros Hadjicostas, Jan 13 2019

MATHEMATICA

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 *)

CROSSREFS

Cf. A007317, A026118.

Sequence in context: A293830 A073708 A024460 * A063675 A000943 A304966

Adjacent sequences:  A039655 A039656 A039657 * A039659 A039660 A039661

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Emeric Deutsch, Mar 14 2004

STATUS

approved

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Last modified February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)