A190975 a(n) = 8*a(n-1) - 2*a(n-2), with a(0)=0, a(1)=1.

0, 1, 8, 62, 480, 3716, 28768, 222712, 1724160, 13347856, 103334528, 799980512, 6193175040, 47945439296, 371177164288, 2873526435712, 22245857157120, 172219804385536, 1333266720770048, 10321694157389312, 79907019817574400, 618612770225816576

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, May 24 2011

Keywords

• nonn

Comments

a(n+1) equals the number of words of length n over {0,1,2,3,4,5,6,7} avoiding 01 and 02. - Milan Janjic, Dec 17 2015

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Tomislav Doslic, Planar polycyclic graphs and their Tutte polynomials, Journal of Mathematical Chemistry, Volume 51, Issue 6, 2013, pp. 1599-1607. See Cor. 3.7(e).
• Index entries for linear recurrences with constant coefficients, signature (8, -2).

Crossrefs

Cf. A190958 (index to generalized Fibonacci sequences).

Programs

Magma

I:=[0,1]; [n le 2 select I[n] else 8*Self(n-1)-2*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Dec 17 2015

Mathematica

LinearRecurrence[{8,-2}, {0,1}, 50]

PARI

Vec(1/(1-8*x+2*x^2) + O(x^100)) \\ Altug Alkan, Dec 17 2015

Formula

a(n) = ((4 + sqrt(14))^n - (4 - sqrt(14))^n)/(2*sqrt(14)). - Giorgio Balzarotti, May 28 2011

G.f.: x/(1 - 8x + 2*x^2). - Philippe Deléham, Oct 12 2011

E.g.f.: (1/sqrt(14))*exp(4*x)*sinh(sqrt(14)*x). - G. C. Greubel, Dec 18 2015