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%I #25 Oct 19 2022 08:10:23
%S 0,10,53,153,334,620,1035,1603,2348,3294,4465,5885,7578,9568,11879,
%T 14535,17560,20978,24813,29089,33830,39060,44803,51083,57924,65350,
%U 73385,82053,91378,101384,112095,123535,135728,148698,162469,177065,192510,208828,226043
%N Number of triples (i,j,k) such that i+j+k > 0 with -n <= i,j,k <= n.
%C If we add the triples (i,j,k) such that i+j+k >= 0 then the corresponding numbers seem to be those of A130748.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1)
%F From _Alois P. Heinz_, Apr 08 2018: (Start)
%F a(n) = n*(3+9*n+8*n^2)/2.
%F G.f.: (x^2+13*x+10)*x/(x-1)^4.
%F a(n) = A130748(n) - A003215(n) for n > 0. (End)
%t a[n_]:=Total[Flatten[Table[Table[Table[If[i+j+k>0,1,0],{i,-n,n}],{j,-n,n}],{k,-n,n}]]];
%t Table[a[n],{n,0,32}]
%o (PARI) a(n) = n*(3+9*n+8*n^2)/2; \\ _Altug Alkan_, Apr 08 2018
%Y Cf. A003215, A130748.
%K nonn,easy
%O 0,2
%A _Andres Cicuttin_, Apr 05 2018
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