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%I #8 Jan 28 2021 21:20:56
%S 0,1,4,25,52,170,280,674,984,1979,2684,4795,6188,10164,12656,19524,
%T 23664,34773,41268,58333,68068,93214,107272,143078,162760,212303,
%U 239148,306047,341852,430312,477152,592008,652256,799017,875364,1060257,1155732,1385746,1503736
%N a(n) = Sum_{k=1..floor(n/2)} k^2 * (n-k)^2.
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,5,-5,-10,10,10,-10,-5,5,1,-1).
%F G.f.: x^2*(1+3*x+16*x^2+12*x^3+23*x^4+5*x^5+4*x^6)/((1-x)^6*(1+x)^5).
%F a(n) = (2*n-1+(-1)^n)*(2*n+3+(-1)^n)*(16*n^3-n^2+10*n-4-(n^2+6*n+4)*(-1)^n)/3840.
%F a(n) = a(n-1) + 5*a(n-2) - 5*a(n-3) - 10*a(n-4) + 10*a(n-5) + 10*a(n-6) - 10*a(n-7) - 5*a(n-8) + 5*a(n-9) + a(n-10) - a(n-11).
%e a(6) = 1^2*5^2 + 2^2*4^2 + 3^2*3^2 = 25 + 64 + 81 = 170.
%t CoefficientList[Series[x (1 + 3 x + 16 x^2 + 12 x^3 + 23 x^4 + 5 x^5 + 4 x^6)/((1 - x)^6 (1 + x)^5), {x, 0, 80}], x]
%Y Cf. A023855.
%K nonn,easy
%O 1,3
%A _Wesley Ivan Hurt_, Jan 28 2021
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