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A190981
a(n) = 9*a(n-1) - 4*a(n-2), with a(0)=0, a(1)=1.
2
0, 1, 9, 77, 657, 5605, 47817, 407933, 3480129, 29689429, 253284345, 2160801389, 18434075121, 157263470533, 1341634934313, 11445660526685, 97644405002913, 833017002919477, 7106575406263641, 60627110644694861, 517217694177199185, 4412450805016013221
OFFSET
0,3
FORMULA
G.f.: x/(1-9x+4*x^2). - Philippe Deléham, Oct 12 2011
E.g.f.: (2/sqrt(65))*exp(9*x/2)*sinh(sqrt(65)*x/2). - G. C. Greubel, Aug 25 2022
MATHEMATICA
LinearRecurrence[{9, -4}, {0, 1}, 50]
PROG
(Magma) [2^(n-1)*Evaluate(ChebyshevU(n), 9/4): n in [0..30]]; // G. C. Greubel, Aug 25 2022
(SageMath)
A190981 = BinaryRecurrenceSequence(9, -4, 0, 1)
[A190981(n) for n in (0..30)] # G. C. Greubel, Aug 25 2022
CROSSREFS
Cf. A190958 (index to generalized Fibonacci sequences).
Sequence in context: A266125 A290708 A126631 * A254659 A346847 A355372
KEYWORD
nonn,easy
AUTHOR
STATUS
approved