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A055271
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a(n) = 5*a(n-1) - a(n-2) with a(0)=1, a(1)=7.
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4
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1, 7, 34, 163, 781, 3742, 17929, 85903, 411586, 1972027, 9448549, 45270718, 216905041, 1039254487, 4979367394, 23857582483, 114308545021, 547685142622, 2624117168089, 12572900697823, 60240386321026, 288629030907307, 1382904768215509, 6625894810170238, 31746569282635681, 152106951603008167
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OFFSET
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0,2
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 122-125, 194-196.
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LINKS
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FORMULA
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a(n) = (7*(((5+sqrt(21))/2)^n - ((5-sqrt(21))/2)^n) - (((5+sqrt(21))/2)^(n-1) - ((5-sqrt(21))/2)^(n-1)))/sqrt(21).
G.f.: (1+2*x)/(1-5*x+x^2).
a(n) = ChebyshevT(n, 5/2) + (9/2)*ChebyshevU(n-1,5/2) = ChebyshevU(n, 5/2) + 2*ChebyshevU(n-1, 5/2). - G. C. Greubel, Mar 16 2020
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MAPLE
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MATHEMATICA
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LinearRecurrence[{5, -1}, {1, 7}, 30] (* G. C. Greubel, Mar 16 2020 *)
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PROG
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(Magma) I:=[1, 7]; [n le 2 select I[n] else 5*Self(n-1) - Self(n-2): n in [1..30]]; // G. C. Greubel, Mar 16 2020
(Sage) [chebyshev_U(n, 5/2) + 2*chebyshev_U(n-1, 5/2) for n in (0..30)] # G. C. Greubel, Mar 16 2020
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CROSSREFS
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KEYWORD
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easy,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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