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A123011
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a(n) = 2*a(n-1) + 5*a(n-2) for n > 1; a(0) = 1, a(1) = 5.
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5
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1, 5, 15, 55, 185, 645, 2215, 7655, 26385, 91045, 314015, 1083255, 3736585, 12889445, 44461815, 153370855, 529050785, 1824955845, 6295165615, 21715110455, 74906048985, 258387650245, 891305545415, 3074549342055
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = ((3+2*sqrt(6))*(1+sqrt(6))^n + (3-2*sqrt(6))*(1-sqrt(6))^n)/6. - Klaus Brockhaus, Aug 15 2009
G.f.: (1+3*x)/(1-2*x-5*x^2).
Inverse binomial transform of A164549. (End)
a(n) = (sqrt(5)*i)^(n-1)*(sqrt(5)*i*ChebyshevU(n, -i/sqrt(5)) + 3*ChebyshevU(n-1, -i/sqrt(5))) for n > 0 with a(0) = 1. - G. C. Greubel, Jul 13 2021
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MATHEMATICA
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LinearRecurrence[{2, 5}, {1, 5}, 31] (* G. C. Greubel, Jul 13 2021 *)
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PROG
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(Magma) [ n le 2 select 4*n-3 else 2*Self(n-1)+5*Self(n-2): n in [1..24] ]; - Klaus Brockhaus, Aug 15 2009
(Sage) [1]+[(sqrt(5)*i)^(n-1)*(sqrt(5)*i*chebyshev_U(n, -i/sqrt(5)) + 3*chebyshev_U(n-1, -i/sqrt(5))) for n in (1..30)] # G. C. Greubel, Jul 13 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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