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A084157
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a(n) = 8*a(n-1) - 16*a(n-2) + 12*a(n-4) with a(0)=0, a(1)=1, a(2)=4, a(3)=22.
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2
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0, 1, 4, 22, 112, 556, 2704, 13000, 62080, 295312, 1401664, 6644320, 31472896, 149017792, 705395968, 3338614912, 15800258560, 74772443392, 353840161792, 1674425579008, 7923565146112, 37494981225472, 177428889407488
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = 8*a(n-1) - 16*a(n-2) + 12*a(n-4).
a(n) = ((3+sqrt(3))^n + (3-sqrt(3))^n - (1+sqrt(3))^n - (1-sqrt(3))^n)/4.
G.f.: x*(1-4*x+6*x^2)/((1-2*x-2*x^2)*(1-6*x+6*x^2)).
E.g.f.: exp(2*x)*sinh(x)*cosh(sqrt(3)*x).
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MATHEMATICA
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LinearRecurrence[{8, -16, 0, 12}, {0, 1, 4, 22}, 30] (* Harvey P. Dale, Feb 19 2017 *)
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PROG
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(Magma) I:=[0, 1, 4, 22]; [n le 4 select I[n] else 8*Self(n-1) -16*Self(n-2) +12*Self(n-4): n in [1..41]]; // G. C. Greubel, Oct 11 2022
(SageMath)
A083881 = BinaryRecurrenceSequence(6, -6, 1, 3)
A026150 = BinaryRecurrenceSequence(2, 2, 1, 1)
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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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