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A190976 a(n) = 8*a(n-1) - 3*a(n-2), with a(0)=0, a(1)=1. 4
0, 1, 8, 61, 464, 3529, 26840, 204133, 1552544, 11807953, 89805992, 683024077, 5194774640, 39509124889, 300488675192, 2285382026869, 17381590189376, 132196575434401, 1005427832907080, 7646832936953437, 58158379996906256, 442326541164389737 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = ((4 + sqrt(13))^n - (4 - sqrt(13))^n)/(2*sqrt(13)). - Giorgio Balzarotti, May 28 2011
G.f.: x/(1 - 8*x + 3*x^2). - Philippe Deléham, Oct 12 2011
From G. C. Greubel, Jun 11 2022: (Start)
a(n) = 3^((n-1)/2)*ChebyshevU(n-1, 4/sqrt(3)).
E.g.f.: (1/sqrt(13))*exp(4*x)*sinh(sqrt(13)*x). (End)
MATHEMATICA
LinearRecurrence[{8, -3}, {0, 1}, 50]
PROG
(Magma) [n le 2 select n-1 else 8*Self(n-1) - 3*Self(n-2): n in [1..51]]; // G. C. Greubel, Jun 11 2022
(SageMath) [lucas_number1(n, 8, 3) for n in (0..50)] # G. C. Greubel, Jun 11 2022
CROSSREFS
Cf. A190958 (index to generalized Fibonacci sequences).
Sequence in context: A283410 A081907 A278596 * A254602 A363571 A361772
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)