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A271114 Expansion of (1+x)*(2+x)/(1-x)^2.

%I A271114 #33 Mar 11 2024 01:45:32
%S A271114 2,7,13,19,25,31,37,43,49,55,61,67,73,79,85,91,97,103,109,115,121,127,
%T A271114 133,139,145,151,157,163,169,175,181,187,193,199,205,211,217,223,229,
%U A271114 235,241,247,253,259,265,271,277,283,289,295,301,307,313,319,325
%N A271114 Expansion of (1+x)*(2+x)/(1-x)^2.
%H A271114 Colin Barker, <a href="/A271114/b271114.txt">Table of n, a(n) for n = 0..1000</a>
%H A271114 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A271114 G.f.: (1+x)*(2+x)/(1-x)^2.
%F A271114 a(n) = A270700(n)/6.
%F A271114 a(n) = 6*n+1 = A016921(n) for n>0.
%F A271114 a(n) = 2*a(n-1)-a(n-2) for n>2.
%F A271114 E.g.f.: 1 + (1+6*x)*exp(x). - _G. C. Greubel_, Mar 31 2016
%F A271114 From _Bruno Berselli_ and _G. C. Greubel_, Mar 31 2016: (Start)
%F A271114 a(5*m+1) = 30*m + 7 = A132231(m+1).
%F A271114 a(5*m+2) = 30*m + 13 = A082369(m+1).
%F A271114 a(5*m+3) = 30*m + 19 = A156376(m).
%F A271114 a(5*m+4) = 30*m + 25 = 5*A016969(m).
%F A271114 a(5*m+5) = 30*m + 31 = A128470(m+1). (End)
%F A271114 a(n) = A100764(n+3) for n >= 1. - _Georg Fischer_, Oct 30 2018
%t A271114 Join[{2}, LinearRecurrence[{2, -1}, {7, 13}, 100]] (* _G. C. Greubel_, Mar 31 2016 *)
%o A271114 (PARI) Vec((1+x)*(2+x)/(1-x)^2 + O(x^70))
%Y A271114 Cf. A016921, A270700.
%Y A271114 Cf. A016969, A082369, A100764, A128470, A132231, A156376.
%K A271114 nonn,easy
%O A271114 0,1
%A A271114 _Colin Barker_, Mar 31 2016