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A021503
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Expansion of 1/((1-x)(1-3x)(1-6x)(1-8x)).
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1
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1, 18, 217, 2214, 20701, 183906, 1582129, 13325598, 110626021, 909165114, 7418351161, 60217256502, 486961532461, 3927035533842, 31604351090113, 253963231160526, 2038476448492021, 16348435376893290
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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) = (3*8^(n+3)-7*6^(n+3)+7*3^(n+3)-3)/210. - Yahia Kahloune, May 06 2013
a(0)=1, a(1)=18; for n>1, a(n) = 14*a(n-1) -48*a(n-2) +(3^n -1)/2. - Vincenzo Librandi, Jul 10 2013
a(0)=1, a(1)=18, a(2)=217, a(3)=2214; for n>3, a(n) = 18*a(n-1) -107*a(n-2) +234*a(n-3) -144*a(n-4). - Vincenzo Librandi, Jul 10 2013
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MATHEMATICA
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CoefficientList[Series[1 / ((1 - x) (1 - 3 x)(1 - 6 x) (1 - 8 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 10 2013 *)
LinearRecurrence[{18, -107, 234, -144}, {1, 18, 217, 2214}, 20] (* Harvey P. Dale, Mar 05 2022 *)
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PROG
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(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-6*x)*(1-8*x)))); /* or */ I:=[1, 18, 217, 2214]; [n le 4 select I[n] else 18*Self(n-1)-107*Self(n-2)+234*Self(n-3)-144*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 10 2013
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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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