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A190959
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a(n) = 3*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1.
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2
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0, 1, 3, 4, -3, -29, -72, -71, 147, 796, 1653, 979, -5328, -20879, -35997, -3596, 169197, 525571, 730728, -435671, -4960653, -12703604, -13307547, 23595379, 137323872, 293994721, 195364803, -883879196, -3628461603, -6465988829, -1255658472, 28562968729
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OFFSET
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0,3
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COMMENTS
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This is the Lucas U(P=3, Q=5) sequence. - R. J. Mathar, Oct 24 2012
a(n+2)/a(n+1) equals the continued fraction 3 - 5/(3 - 5/(3 - 5/(3 - ... - 5/3))) with n 5's. - Greg Dresden, Oct 06 2019
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LINKS
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FORMULA
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E.g.f.: 2*exp(3*x/2)*sin(sqrt(11)*x/2)/sqrt(11). - Stefano Spezia, Oct 06 2019
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MATHEMATICA
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LinearRecurrence[{3, -5}, {0, 1}, 50]
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PROG
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(PARI) x='x+O('x^30); concat([0], Vec(x/(1-3x+5*x^2))) \\ G. C. Greubel, Jan 25 2018
(Magma) I:=[0, 1]; [n le 2 select I[n] else 3*Self(n-1) - 5*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 25 2018
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CROSSREFS
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Cf. A190958 (index to generalized Fibonacci sequences), A190970 (binomial transf.), A106852 (inv. bin. transf., shifted).
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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