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a(n) = floor(Sum_{1<=i<j<=n} (sqrt(j)-sqrt(i))^2).
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%I #8 Mar 30 2023 18:15:00

%S 0,0,2,4,8,14,22,32,45,61,80,103,130,162,198,239,286,338,397,462,533,

%T 612,698,791,893,1003,1122,1250,1387,1534,1691,1858,2036,2225,2426,

%U 2638,2862,3098,3348,3610,3885,4175,4478,4796,5128,5476,5838,6217,6611,7022,7450,7894

%N a(n) = floor(Sum_{1<=i<j<=n} (sqrt(j)-sqrt(i))^2).

%t Table[Floor[Sum[(Sqrt[j]-Sqrt[i])^2,{i,n},{j,i+1,n}]],{n,2,53}] (* _Stefano Spezia_, Mar 30 2023 *)

%K nonn

%O 2,3

%A _Clark Kimberling_