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%I #9 Apr 08 2014 14:06:22
%S 1,3,18,70,285,1533,7084,29604,116385,419815,1385142,4278066,12678757,
%T 36517950,102364200,278451568,733599079,1872496417,4639365470,
%U 11183927650,26287242751,60341512253,135432776524,297482865100
%N Half the number of length n integer sequences with sum zero and sum of squares 18.
%H R. H. Hardin, <a href="/A157535/b157535.txt">Table of n, a(n) for n=2..50</a>
%F [cache enabling] count(n,s,ss)->count(n,t,tt) where t=s mod n, q=(t-s)/n, tt=ss+2*q*s+n*q^2; count(n,t,tt)=sum[i^2<=tt]{ count(n-1,t-i,tt-i^2) }. a(n)=count(n,0,18)/2.
%F G.f.: -x^2*(434*x^16 +19697*x^15 +99303*x^14 -116957*x^13 -153862*x^12 +406284*x^11 -362744*x^10 +160940*x^9 -16710*x^8 -25990*x^7 +20878*x^6 -9354*x^5 +3002*x^4 -728*x^3 +132*x^2 -16*x +1) / (x -1)^19. - _Colin Barker_, Apr 08 2014
%K nonn,easy
%O 2,2
%A _R. H. Hardin_, Mar 02 2009