%I #16 Sep 08 2022 08:44:45
%S 1,14,133,1086,8253,60438,433861,3080462,21737485,152860422,
%T 1072817109,7520900478,52691034397,369016181366,2583829064677,
%U 18089666698734,126639120006189,886519652765670,6205820820773365
%N Expansion of 1/((1-x)(1-2x)(1-4x)(1-7x)).
%H Vincenzo Librandi, <a href="/A021079/b021079.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 (14,-63,106,-56).
%F a(n) = -(1/18)+(4/5)*2^n-(32/9)*4^n+(343/90)*7^n. [_Antonio Alberto Olivares_, May 22 2012]
%F 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
%F 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
%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 4 x) (1 - 7 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 06 2013 *)
%t LinearRecurrence[{14, -63, 106, -56}, {1, 14, 133, 1086}, 20] (* _Robert G. Wilson v_, Jul 06 2013 *)
%o (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
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.