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A213042 Convolution of (1,0,2,0,3,0,...) and (1,0,0,2,0,0,3,0,0,...); i.e., (A027656(n)) and (A175676(n+2)).

%I A213042 #18 Jul 17 2017 00:43:55
%S A213042 1,0,2,2,3,4,7,6,11,12,15,18,24,24,33,36,42,48,58,60,74,80,90,100,115,
%T A213042 120,140,150,165,180,201,210,237,252,273,294,322,336,371,392,420,448,
%U A213042 484,504,548,576,612,648,693,720,774,810,855,900,955,990,1055
%N A213042 Convolution of (1,0,2,0,3,0,...) and (1,0,0,2,0,0,3,0,0,...); i.e., (A027656(n)) and (A175676(n+2)).
%H A213042 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,2,-1,-4,-1,2,2,0,-1).
%F A213042 a(n) = 2*a(n-2)+2*a(n-3)-a(n-4)-4*a(n-5)-a(n-6)+2*a(n-7)+2*a(n-8)-a(n-10).
%F A213042 G.f.: 1/(((1 - x^2)^2)*(1 - x^3)^2).
%e A213042 a(6) = (1,0,2,0,3,0,4)**(1,0,0,2,0,0,3) = 1*3 + 0*0 + 2*0 + 0*2 + 3*0 + 0*0 + 4*1 = 7.
%t A213042 s = Normal[Series[1/((1 - x^2)^2 (1 - x^3)^2),
%t A213042 {x, 0, 80}]]
%t A213042 c = CoefficientList[s, t]  (* A213042 *)
%K A213042 nonn,easy
%O A213042 0,3
%A A213042 _Clark Kimberling_, Jun 10 2012