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A021079
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Expansion of 1/((1-x)(1-2x)(1-4x)(1-7x)).
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1
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1, 14, 133, 1086, 8253, 60438, 433861, 3080462, 21737485, 152860422, 1072817109, 7520900478, 52691034397, 369016181366, 2583829064677, 18089666698734, 126639120006189, 886519652765670, 6205820820773365
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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(0)=1, a(1)=14; for n>1, a(n) = 11*a(n-1) -28*a(n-2) +2^n - 1. - Vincenzo Librandi, Jul 06 2013
a(0)=1, a(1)=14, a(2)=133, a(3)=1086; for n>3, a(n) = 14*a(n-1) -63*a(n-2) +106*a(n-3) -56*a(n-4). - Vincenzo Librandi, Jul 06 2013
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MATHEMATICA
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CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 4 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 06 2013 *)
LinearRecurrence[{14, -63, 106, -56}, {1, 14, 133, 1086}, 20] (* Robert G. Wilson v, Jul 06 2013 *)
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PROG
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(Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-4*x)*(1-7*x)))); /* or */ I:=[1, 14, 133, 1086]; [n le 4 select I[n] else 14*Self(n-1)-63*Self(n-2)+106*Self(n-3)-56*Self(n-4): n in [1..25]]; // Vincenzo Librandi, Jul 06 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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