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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)).
1

%I #18 Jul 17 2017 00:43:55

%S 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 120,140,150,165,180,201,210,237,252,273,294,322,336,371,392,420,448,

%U 484,504,548,576,612,648,693,720,774,810,855,900,955,990,1055

%N 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 <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 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 G.f.: 1/(((1 - x^2)^2)*(1 - x^3)^2).

%e 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 s = Normal[Series[1/((1 - x^2)^2 (1 - x^3)^2),

%t {x, 0, 80}]]

%t c = CoefficientList[s, t] (* A213042 *)

%K nonn,easy

%O 0,3

%A _Clark Kimberling_, Jun 10 2012