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A084134
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a(n) = 8*a(n-1) - 6*a(n-2), a(0) = 1, a(1) = 4.
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4
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1, 4, 26, 184, 1316, 9424, 67496, 483424, 3462416, 24798784, 177615776, 1272133504, 9111373376, 65258185984, 467397247616, 3347628865024, 23976647434496, 171727406285824, 1229959365679616, 8809310487721984
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = (4+sqrt(10))^n/2 + (4-sqrt(10))^n/2.
G.f.: (1-4*x)/(1 - 8*x + 6*x^2).
E.g.f.: exp(4*x)*cosh(sqrt(10)*x).
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MATHEMATICA
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LinearRecurrence[{8, -6}, {1, 4}, 30] (* Harvey P. Dale, Nov 30 2011 *)
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PROG
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(Magma) [n le 2 select 4^(n-1) else 8*Self(n-1) -6*Self(n-2): n in [1..40]]; // G. C. Greubel, Oct 13 2022
(SageMath)
A084134=BinaryRecurrenceSequence(8, -6, 1, 4)
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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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STATUS
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approved
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