A200864 - OEIS

%I #29 Mar 29 2024 05:43:45

%S 1,7,42,230,1211,6237,31732,160300,806421,4046867,20278622,101525970,

%T 508028431,2541337897,12710276712,63562145240,317843011241,

%U 1589311911327,7946850122002,39735122306110,198678226618851,993398978359157,4967018427590492,24835162745336580

%N Expansion of 1/((1+x)*(1-3*x)*(1-5*x)).

%H Bruno Berselli, <a href="/A200864/b200864.txt">Table of n, a(n) for n = 0..1000</a>.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,-15).

%F G.f.: 1/((1+x)*(1-3*x)*(1-5*x)).

%F a(n) = (50*5^n-27*3^n+(-1)^n)/24.

%F a(n) = 2*a(n-1)+3*a(n-2)+5^n for n>1, a(0)=1, a(1)=7.

%F a(n) = 7*a(n-1)-7*a(n-2)-15*a(n-3) for n>2, a(0)=1, a(1)=7, a(2)=42.

%F a(n+1)+a(n) = A005059(n+2).

%F a(n+2)-a(n) = A081625(n+2).

%t CoefficientList[Series[1/((1+x)(1-3x)(1-5x)), {x, 0, 24}], x]

%t LinearRecurrence[{7,-7,-15},{1,7,42},30] (* _Harvey P. Dale_, May 26 2015 *)

%o (PARI) Vec(1/((1+x)*(1-3*x)*(1-5*x))+O(x^24))

%o (Magma) m:=24; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1+x)*(1-3*x)*(1-5*x))));

%o (Maxima) makelist(coeff(taylor(1/((1+x)*(1-3*x)*(1-5*x)), x, 0, n), x, n), n, 0, 23);

%Y Cf. A016209, A200859.

%K nonn,easy

%O 0,2

%A _Bruno Berselli_, Nov 23 2011