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 A019869 Expansion of 1/((1-5*x)*(1-6*x)*(1-12*x)). 1
 1, 23, 367, 5075, 65551, 817643, 10013527, 121451315, 1465540351, 17637184763, 211960186087, 2545454874755, 30557298487951, 366759842503883, 4401557777453047, 52821361851453395, 633872505937432351 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is the number of partitions of n into parts 5, 6, and 12. - Joerg Arndt, Apr 29 2017 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Index entries for linear recurrences with constant coefficients, signature (23,-162,360). FORMULA 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 a(n) = 18*a(n-1) -72*a(n-2) +5^n. - Vincenzo Librandi, Jul 03 2013 MAPLE A019869:=n->25*5^n/7-6*6^n+24*12^n/7: seq(A019869(n), n=0..25); # Wesley Ivan Hurt, Apr 28 2017 MATHEMATICA 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 *) PROG (MAGMA) m:=20; R:=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 CROSSREFS Sequence in context: A021844 A019672 A021629 * A021294 A019628 A018091 Adjacent sequences:  A019866 A019867 A019868 * A019870 A019871 A019872 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified September 28 01:27 EDT 2021. Contains 347698 sequences. (Running on oeis4.)