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A190975
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a(n) = 8*a(n-1) - 2*a(n-2), with a(0)=0, a(1)=1.
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4
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0, 1, 8, 62, 480, 3716, 28768, 222712, 1724160, 13347856, 103334528, 799980512, 6193175040, 47945439296, 371177164288, 2873526435712, 22245857157120, 172219804385536, 1333266720770048, 10321694157389312, 79907019817574400, 618612770225816576
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OFFSET
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0,3
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COMMENTS
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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
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LINKS
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FORMULA
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a(n) = ((4 + sqrt(14))^n - (4 - sqrt(14))^n)/(2*sqrt(14)). - Giorgio Balzarotti, May 28 2011
E.g.f.: (1/sqrt(14))*exp(4*x)*sinh(sqrt(14)*x). - G. C. Greubel, Dec 18 2015
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MATHEMATICA
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LinearRecurrence[{8, -2}, {0, 1}, 50]
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PROG
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(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
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CROSSREFS
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Cf. A190958 (index to generalized Fibonacci sequences).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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