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A019869
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Expansion of 1/((1-5*x)*(1-6*x)*(1-12*x)).
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1
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1, 23, 367, 5075, 65551, 817643, 10013527, 121451315, 1465540351, 17637184763, 211960186087, 2545454874755, 30557298487951, 366759842503883, 4401557777453047, 52821361851453395, 633872505937432351
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of partitions of n into parts 5, 6, and 12. - Joerg Arndt, Apr 29 2017
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LINKS
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FORMULA
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G.f.: 1/((1-5*x)*(1-6*x)*(1-12*x)).
a(n) = 25*5^n/7-6*6^n+24*12^n/7. - R. J. Mathar, Jun 29 2013
a(0)=1, a(1)=23, a(2)=367; for n>2, a(n) = 23*a(n-1) -162*a(n-2) +360*a(n-3). - Vincenzo Librandi, Jul 03 2013
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MAPLE
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MATHEMATICA
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CoefficientList[Series[1 / ((1 - 5 x) (1 - 6 x) (1 - 12 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Jul 03 2013 *)
LinearRecurrence[{23, -162, 360}, {1, 23, 367}, 20] (* Harvey P. Dale, Aug 04 2020 *)
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PROG
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(Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-5*x)*(1-6*x)*(1-12*x)))); /* or */ I:=[1, 23, 367]; [n le 3 select I[n] else 23*Self(n-1)-162*Self(n-2)+360*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 03 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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