

A036759


Number of mirrorsymmetrical edgerooted treelike octagonal systems.


8



1, 1, 3, 4, 15, 23, 94, 155, 661, 1139, 4983, 8844, 39362, 71360, 321561, 592361, 2694421, 5025849, 23029195, 43388208, 199990961, 379900479, 1759636142, 3365582261, 15652514944, 30112397278, 140531706444, 271707661708
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OFFSET

1,3


REFERENCES

S. J. Cyvin, B. N. Cyvin, and J. Brunvoll, Enumeration of treelike octagonal systems: catapolyoctagons, ACH Models in Chem. 134(1) (1997), 5570. [The index of summation in Eq. (15), p. 60, should start at i = 0, not at i = 1.  Petros Hadjicostas, Jul 30 2019]


LINKS

Table of n, a(n) for n=1..28.
J. Brunvoll, S. J. Cyvin, and B. N. Cyvin, Enumeration of treelike octagonal systems, J. Math. Chem., 21 (1997), 193196.


FORMULA

G.f. V=V(x) satisfies x(x2)V^3 + 2(x^23x+1)V^2 + (x^23x+2)V  x(x+2) = 0.
From Petros Hadjicostas, Jul 30 2019: (Start)
Let U(0) = 1 and U(n) = A036758(n) for n >= 1. Let also a(0) = a(1) = 1 (even though the offset for the current sequence is 1 as it is done in Table II (p. 61) in Cyvin et al. (1997) and in Eq. (5), p. 195, in Brunvoll et al. (1997)).
Then
a(n) = Sum_{i = 0..floor((n1)/2)} U(i) * a(n12*i) for n even >= 2, and
a(n) = U((n1)/2) + Sum_{i = 0..floor((n1)/2)} U(i) * a(n12*i) for n odd >= 3.
This is Eq. (15), p. 60, in Cyvin et al. (1997), but we have corrected the lower index of summation (from i = 1 to i = 0).
(End)


MAPLE

F := (2+3*V+6*V^2+2*V^3(V+2)*sqrt(1+4*V+8*V^2+4*V^4))/2/(V^3+2*V^2V1): Order := 40: S := solve(series(F, V)=x, V);


PROG

(PARI) a(n)=if(n<1, 0, polcoeff(serreverse((2*x^3+6*x^2+3*x+2(x+2)*sqrt(4*x^4+8*x^2+4*x+1+x*O(x^n)))/2/(x^3+2*x^2x1)), n)) /* Michael Somos, Mar 10 2004 */


CROSSREFS

Cf. A036758, A036760, A121112, A121113, A121114.
Sequence in context: A109926 A272514 A065942 * A263718 A286675 A286025
Adjacent sequences: A036756 A036757 A036758 * A036760 A036761 A036762


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Emeric Deutsch, Feb 28 2004


STATUS

approved



