A228605 The Merrifield-Simmons index of the meta-polyphenylene chain of length n.

1, 18, 299, 4982, 83001, 1382818, 23038099, 383820582, 6394548401, 106534800818, 1774896845499, 29570232336982, 492647582692201, 8207633878782018, 136741265470126499, 2278144220188626182, 37954461443189410401, 632330969513105454418, 10534794588084770785099

Offset

0,2

Comments

The Merrifield-Simmons index of a graph is the number of its independent vertex subsets.

References

R. E. Merrifield, H. E. Simmons, Topological Methods in Chemistry, Wiley, New York, 1989.

Links

Table of n, a(n) for n=0..18.

T. Doslic, M. S. Litz, Matchings and independent sets in polyphenylene chains, MATCH, Commun. Math. Comput. Chem., 67, 2012, 313-330.

Index entries for linear recurrences with constant coefficients, signature (16,11).

Formula

a(n) = (((2+sqrt(3))*(8+5*sqrt(3))^n - (2-sqrt(3))*(8-5*sqrt(3))^n)*(1/2))/sqrt(3).

G.f.: (1+2*x)/(1-16*x -11*x^2).

Maple

gser := series((2*x+1)/(1-16*x-11*x^2), x = 0, 22): seq(coeff(gser, x, n), n = 0 .. 20);

Crossrefs

Cf. A228604, A228606.

Sequence in context: A113367 A228604 A228606 * A193317 A161599 A273434

Adjacent sequences: A228602 A228603 A228604 * A228606 A228607 A228608

Keyword

nonn,easy

Author

Emeric Deutsch, Nov 23 2013

Status

approved