This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A200864 #29 Mar 29 2024 05:43:45
%S A200864 1,7,42,230,1211,6237,31732,160300,806421,4046867,20278622,101525970,
%T A200864 508028431,2541337897,12710276712,63562145240,317843011241,
%U A200864 1589311911327,7946850122002,39735122306110,198678226618851,993398978359157,4967018427590492,24835162745336580
%N A200864 Expansion of 1/((1+x)*(1-3*x)*(1-5*x)).
%H A200864 Bruno Berselli, <a href="/A200864/b200864.txt">Table of n, a(n) for n = 0..1000</a>.
%H A200864 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,-15).
%F A200864 G.f.: 1/((1+x)*(1-3*x)*(1-5*x)).
%F A200864 a(n) = (50*5^n-27*3^n+(-1)^n)/24.
%F A200864 a(n) = 2*a(n-1)+3*a(n-2)+5^n for n>1, a(0)=1, a(1)=7.
%F A200864 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 A200864 a(n+1)+a(n) = A005059(n+2).
%F A200864 a(n+2)-a(n) = A081625(n+2).
%t A200864 CoefficientList[Series[1/((1+x)(1-3x)(1-5x)), {x, 0, 24}], x]
%t A200864 LinearRecurrence[{7,-7,-15},{1,7,42},30] (* _Harvey P. Dale_, May 26 2015 *)
%o A200864 (PARI) Vec(1/((1+x)*(1-3*x)*(1-5*x))+O(x^24))
%o A200864 (Magma) m:=24; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1+x)*(1-3*x)*(1-5*x))));
%o A200864 (Maxima) makelist(coeff(taylor(1/((1+x)*(1-3*x)*(1-5*x)), x, 0, n), x, n), n, 0, 23);
%Y A200864 Cf. A016209, A200859.
%K A200864 nonn,easy
%O A200864 0,2
%A A200864 _Bruno Berselli_, Nov 23 2011