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A212337
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Expansion of 1/(1-4*x+3*x^2)^2.
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2
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1, 8, 42, 184, 731, 2736, 9844, 34448, 118101, 398584, 1328606, 4384392, 14348911, 46633952, 150663528, 484275616, 1549681961, 4939611240, 15690529810, 49686677720, 156905298051, 494251688848, 1553362450652, 4871909504304, 15251194969981, 47659984281176
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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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FORMULA
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EXAMPLE
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a(0) = 1*1 = 1;
a(1) = 1*4 + 4*1 = 8;
a(2) = 1*13 + 4*4 + 13*1 = 42;
a(3) = 1*40 + 4*13 + 13*4 + 40*1 = 184;
a(4) = 1*121 + 4*40 + 13*13 + 40*4 + 121*1 = 731; etc. - Philippe Deléham, Mar 07 2014
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MATHEMATICA
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Table[1 + n ((1 + 9 3^n)/4), {n, 0, 25}] (* Bruno Berselli, May 11 2012 *)
CoefficientList[Series[1/(1-4x+3x^2)^2, {x, 0, 30}], x] (* or *) LinearRecurrence[ {8, -22, 24, -9}, {1, 8, 42, 184}, 30] (* Harvey P. Dale, Jun 14 2020 *)
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PROG
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(Magma) m:=26; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^2*(1-3*x)^2))); // Bruno Berselli, May 11 2012
(PARI) Vec(1/(1-4*x+3*x^2)^2 + O(x^100)) \\ Altug Alkan, Nov 01 2015
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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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