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A139700
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Binomial transform of [1, 30, 30, 30, ...].
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7
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1, 31, 91, 211, 451, 931, 1891, 3811, 7651, 15331, 30691, 61411, 122851, 245731, 491491, 983011, 1966051, 3932131, 7864291, 15728611, 31457251, 62914531, 125829091, 251658211, 503316451, 1006632931, 2013265891, 4026531811, 8053063651, 16106127331
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OFFSET
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1,2
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COMMENTS
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The binomial transform of [1, c, c, c, ...] has the terms a(n) = 1 - c + c*2^(n-1) if the offset 1 is chosen. The o.g.f. of the a(n) is x{1+(c-2)x}/{(2x-1)(x-1)}. This applies to A139634 with c=10, to A139635 with c=11, to A139697 with c=12, to A139698 with c=25 and to A099003, A139700, A139701 accordingly. - R. J. Mathar, May 11 2008
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LINKS
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FORMULA
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a(n) = 3*a(n-1) - 2*a(n-2).
G.f.: x*(28*x+1) / ((x-1)*(2*x-1)). (End)
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EXAMPLE
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a(3) = 91 = (1, 2, 1) dot (1, 30, 30) = (1 + 60 + 30).
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MAPLE
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MATHEMATICA
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LinearRecurrence[{3, -2}, {1, 31}, 30] (* Harvey P. Dale, Apr 18 2018 *)
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PROG
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(PARI) Vec(x*(28*x+1)/((x-1)*(2*x-1)) + O(x^100)) \\ Colin Barker, Mar 11 2014
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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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