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A190975
a(n) = 8*a(n-1) - 2*a(n-2), with a(0)=0, a(1)=1.
4
0, 1, 8, 62, 480, 3716, 28768, 222712, 1724160, 13347856, 103334528, 799980512, 6193175040, 47945439296, 371177164288, 2873526435712, 22245857157120, 172219804385536, 1333266720770048, 10321694157389312, 79907019817574400, 618612770225816576
OFFSET
0,3
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
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).
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
MATHEMATICA
LinearRecurrence[{8, -2}, {0, 1}, 50]
PROG
(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
(PARI) Vec(1/(1-8*x+2*x^2) + O(x^100)) \\ Altug Alkan, Dec 17 2015
CROSSREFS
Cf. A190958 (index to generalized Fibonacci sequences).
Sequence in context: A085353 A125396 A163444 * A287815 A244831 A331235
KEYWORD
nonn
AUTHOR
STATUS
approved