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A317974
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a(n) = 2*(a(n-1)+a(n-2)+a(n-3))-a(n-4) for n >= 4, with initial terms 0,0,1,1.
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4
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0, 0, 1, 1, 4, 12, 33, 97, 280, 808, 2337, 6753, 19516, 56404, 163009, 471105, 1361520, 3934864, 11371969, 32865601, 94983348, 274506972, 793339873, 2292794785, 6626299912, 19150362168, 55345573857, 159951677089, 462268926316, 1335981992356, 3861059617665
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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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Lim {n -> infinity} log(a(n))/n = 1.0612750619050... = log(phi+sqrt(phi)) = log(A001622+A139339), where phi is the golden ratio. - A.H.M. Smeets, Sep 04 2018
G.f.: x^2*(1 - x) / (1 - 2*x - 2*x^2 - 2*x^3 + x^4). - Colin Barker, Sep 04 2018
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PROG
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(Python)
a1, a2, a3, a4, n = 1, 1, 0, 0, 3
print(0, 0)
print(1, 0)
print(2, 1)
print(3, 1)
while n < 2172:
....a1, a2, a3, a4, n = 2*(a1+a2+a3)-a4, a1, a2, a3, n+1
(PARI) concat(vector(2), Vec(x^2*(1 - x) / (1 - 2*x - 2*x^2 - 2*x^3 + x^4) + O(x^40))) \\ Colin Barker, Sep 04 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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