|
%I #17 Sep 08 2022 08:44:45
%S 1,15,150,1270,9891,73605,533800,3814140,27018981,190442395,
%T 1338423450,9390536610,65820843271,461096642385,3229086629100,
%U 22609268456680,158287591978761,1108104188689575,7757094081310750
%N Expansion of 1/((1-x)(1-3x)(1-4x)(1-7x)).
%H Vincenzo Librandi, <a href="/A021364/b021364.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (15,-75,145,-84).
%F a(n) = 15*a(n-1) - 75*a(n-2) + 145*a(n-3) - 84*a(n-4), with a(0)=1, a(1)=15, a(2)=150, a(3)=1270. [_Harvey P. Dale_, Jun 09 2011]
%F a(n) = (7^(n+3) - 2*4^(n+4) + 3^(n+5) -2)/72. [_Yahia Kahloune_, Jun 26 2013]
%F a(0)=1, a(1)=15; for n>1, a(n) = 11*a(n-1) -28*a(n-2) +(3^n-1)/2. - _Vincenzo Librandi_, Jul 09 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 3 x) (1 - 4 x) (1 - 7 x)), {x, 0, 20}], x] (* or *) LinearRecurrence[{15, -75, 145, -84}, {1, 15, 150, 1270}, 20] (* _Harvey P. Dale_, Jun 09 2011 *)
%o (Magma) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-3*x)*(1-4*x)*(1-7*x)))); /* or */ I:=[1, 15, 150, 1270]; [n le 4 select I[n] else 15*Self(n-1)-75*Self(n-2)+145*Self(n-3)-84*Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Jul 09 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
|
