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A102303
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a(n) = (1/6) * (7^(n+1) - 3*(-1)^n + 2).
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1
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1, 9, 57, 401, 2801, 19609, 137257, 960801, 6725601, 47079209, 329554457, 2306881201, 16148168401, 113037178809, 791260251657, 5538821761601, 38771752331201, 271402266318409, 1899815864228857, 13298711049602001, 93090977347214001, 651636841430498009
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = 7*a(n-1) + a(n-2) - 7*a(n-3) for n > 2.
G.f.: -(1 + 2*x - 7*x^2)/((1 - x)*(1 + x)*(1 - 7*x)). (End)
E.g.f.: (1/6)*(-3*exp(-x) + 2*exp(x) + 7*exp(7*x)). (End)
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MATHEMATICA
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Table[(7^(n+1) -3*(-1)^n +2)/6, {n, 0, 50}]
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PROG
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(Magma) [(7^(n+1)-3*(-1)^n+2)/6: n in [0..50]]; // G. C. Greubel, Feb 03 2024
(SageMath) [(7^(n+1)-3*(-1)^n+2)/6 for n in range(51)] # G. C. Greubel, Feb 03 2024
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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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EXTENSIONS
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STATUS
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approved
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