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A272525
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Convolution of nonzero repunits (A002275) with themselves.
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13
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1, 22, 343, 4664, 58985, 713306, 8367627, 96021948, 1083676269, 12071330590, 133058984911, 1454046639232, 15775034293553, 170096021947874, 1824417009602195, 19478737997256516, 207133058984910837, 2194787379972565158, 23182441700960219479, 244170096021947873800
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OFFSET
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0,2
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COMMENTS
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LINKS
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Eric Weisstein's World of Mathematics, Repunit
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FORMULA
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O.g.f.: 1/((1 - 10*x)^2*(1 - x)^2).
E.g.f.: (29 + 9*x + 700*exp(9*x) + 9000*x*exp(9*x))*exp(x)/729.
a(n) = 22*a(n-1) - 141*a(n-2) + 220*a(n-3) - 100*a(n-4).
a(n) = (9*n(10^(n+2) + 1) + 7*10^(n+2) + 29)/729.
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MATHEMATICA
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LinearRecurrence[{22, -141, 220, -100}, {1, 22, 343, 4664}, 20]
Table[(9 n (10^(n + 2) + 1) + 7 10^(n + 2) + 29)/729, {n, 0, 19}]
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PROG
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CROSSREFS
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KEYWORD
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base,nonn,easy
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AUTHOR
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STATUS
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approved
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