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A215493
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a(n) = 7*a(n-1) - 14*a(n-2) + 7*a(n-3) with a(0)=0, a(1)=1, a(2)=4.
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17
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0, 1, 4, 14, 49, 175, 637, 2352, 8771, 32928, 124166, 469567, 1779141, 6749211, 25623472, 97329337, 369821228, 1405502182, 5342323441, 20307982135, 77201862045, 293497548512, 1115812645899, 4242135876440, 16128056932078, 61317184775679, 233122447515741
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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)*sqrt(7) = s(1)^(2n-1) + s(2)^(2n-1) + s(4)^(2n-1), where s(j) := 2*Sin(2*Pi*j/7) (for the sums of the respective even powers see A215494, see also A094429, A115146). For the proof of these formula see Witula-Slota's paper.
G.f.: x*(1-3*x)/(1-7*x+14*x^2-7*x^3).
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MATHEMATICA
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LinearRecurrence[{7, -14, 7}, {0, 1, 4}, 50]
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PROG
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(PARI) x='x+O('x^30); concat([0], Vec(x*(1-3*x)/(1-7*x+14*x^2-7*x^3))) \\ G. C. Greubel, Apr 23 2018
(Magma) I:=[0, 1, 4]; [n le 3 select I[n] else 7*Self(n-1) - 14*Self(n-2) +7*Self(n-3): n in [1..30]]; // G. C. Greubel, Apr 23 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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