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A137221
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a(n) = 5*a(n-1) - 9*a(n-2) + 8*a(n-3) - 4*a(n-4), with a(0)=0, a(1)=0, a(2)=0, a(3)=1.
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4
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0, 0, 0, 1, 5, 16, 43, 107, 256, 597, 1365, 3072, 6827, 15019, 32768, 70997, 152917, 327680, 699051, 1485483, 3145728, 6640981, 13981013, 29360128, 61516459, 128625323, 268435456, 559240533, 1163220309, 2415919104, 5010795179
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OFFSET
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0,5
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LINKS
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FORMULA
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O.g.f.: x^3/((1-x+x^2)(1-2*x)^2).
a(n) = (1/3)*(2^(n-1)*(n-2) + ChebyshevU(n, 1/2)). - G. C. Greubel, Jan 05 2022
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MATHEMATICA
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Table[(1/3)*(2^(n-1)*(n-2) + ChebyshevU[n, 1/2]), {n, 0, 40}] (* G. C. Greubel, Jan 05 2022 *)
LinearRecurrence[{5, -9, 8, -4}, {0, 0, 0, 1}, 40] (* Harvey P. Dale, Apr 30 2023 *)
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PROG
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(Magma) [n le 4 select Floor((n-1)/3) else 5*Self(n-1) -9*Self(n-2) +8*Self(n-3) -4*Self(n-4): n in [1..30]]; // G. C. Greubel, Jan 05 2022
(Sage) [(1/3)*(2^(n-1)*(n-2) + chebyshev_U(n, 1/2)) for n in (0..40)] # G. C. Greubel, Jan 05 2022
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CROSSREFS
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Same recurrence as in A100335 (essentially first differences of this sequence).
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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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