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A234279
Number of spanning forests of a benzenoid chain of length n.
1
2, 63, 1984, 62480, 1967616, 61964032, 1951367168, 61452324864, 1935252520960, 60944843472896, 1919270950797312, 60441552929947648, 1903421358545567744, 59942418626579005440, 1887702654313799090176, 59447406240016306798592, 1872113757211501032112128, 58956481730927772118810624
OFFSET
0,1
REFERENCES
Tomislav Doslic, Planar polycyclic graphs and their Tutte polynomials, Journal of Mathematical Chemistry, Volume 51, Issue 6, 2013, pp. 1599-1607.
FORMULA
a(n) = 4^(n-1)*U_{n+1}(4), where U_n(x) is a Chebyshev polynomial of the second kind.
a(n) = 32*a(n-1)-16*a(n-2). G.f.: -(x-2) / (16*x^2-32*x+1). - Colin Barker, Jan 06 2014
MAPLE
t1:=1/(1-2*x*t+t^2);
U:=n->expand(coeff(series(t1, t, 30), t, n));
[seq(4^(n-1)*subs(x=4, U(n+1)), n=0..30)];
PROG
(PARI) Vec(-(x-2)/(16*x^2-32*x+1) + O(x^30)) \\ Colin Barker, Jul 10 2015
CROSSREFS
Sequence in context: A296278 A239744 A024238 * A109667 A330059 A004853
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 28 2013
STATUS
approved