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Expansion of 1/((1-4x)(1-6x)(1-7x)).
2

%I #24 Sep 08 2022 08:44:44

%S 1,17,195,1885,16571,137277,1092715,8456045,64100091,478409437,

%T 3528167435,25777174605,186937014811,1347606967997,9667804397355,

%U 69083038251565,492036007548731,3494997671436957,24769526131110475

%N Expansion of 1/((1-4x)(1-6x)(1-7x)).

%H Vincenzo Librandi, <a href="/A019316/b019316.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (17,-94,168).

%F a(n) = 8*4^n/3 -18*6^n +49*7^n/3. - _R. J. Mathar_, Jun 29 2013

%F a(0)=1, a(1)=17, a(2)=195; for n>2, a(n) = 17*a(n-1) -94*a(n-2) +168*a(n-3). - _Vincenzo Librandi_, Jul 02 2013

%F a(n) = 13*a(n-1) -42*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 02 2013

%p A019316:=n->8*4^n/3 -18*6^n +49*7^n/3: seq(A019316(n), n=0..30); # _Wesley Ivan Hurt_, Jan 27 2017

%t CoefficientList[Series[1 / ((1 - 4 x) (1 - 6 x) (1 - 7 x)), {x, 0, 20}],x] (* _Vincenzo Librandi_, Jul 02 2013 *)

%t LinearRecurrence[{17,-94,168},{1,17,195},30] (* _Harvey P. Dale_, Aug 20 2017 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)*(1-7*x)))); /* or */ I:=[1, 17, 195]; [n le 3 select I[n] else 17*Self(n-1)-94*Self(n-2)+168*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 02 2013

%o (PARI) Vec(1/((1-4*x)*(1-6*x)*(1-7*x)) + O(x^30)) \\ _Michel Marcus_, Jan 28 2017

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_