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A093103
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a(n+2) = 8*a(n+1) + 21*a(n), with a(1)=1, a(2)=8.
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3
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1, 8, 85, 848, 8569, 86360, 870829, 8780192, 88528945, 892615592, 9000032581, 90745188080, 914962188841, 9225346460408, 93016977648925, 937868096859968, 9456301305507169, 95345640478116680, 961347451240583989
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OFFSET
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1,2
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LINKS
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FORMULA
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Limit_{n -> oo} a(n+1)/a(n) converges to 4 + sqrt(37).
a(n) = (i*sqrt(21))^n * ChebyshevU(n, -4*i/sqrt(21)). - G. C. Greubel, Feb 09 2023
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MATHEMATICA
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LinearRecurrence[{8, 21}, {1, 8}, 40] (* Harvey P. Dale, Jan 14 2012 *)
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PROG
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(Magma) [n le 2 select 7*n-6 else 8*Self(n-1) +21*Self(n-2): n in [1..41]]; // G. C. Greubel, Feb 09 2023
(SageMath)
@CachedFunction
if (n<3): return 7*n-6
else: return 8*a(n-1) + 21*a(n-2)
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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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