%I #4 Mar 30 2012 17:40:34

%S 0,1,5,10,19,26,55,46,53,116,86,128,173,145,200,170,221,235,236,305,

%T 341,326,491,425,548,431,676,530,536,635,656,851,905,695,1118,950,

%U 1040,1171,1241,1031,1076,1115,1325,1661,1943,1391,1531,1691,1790,1670,2291,2081

%N a(n) is the smallest number representable in exactly n ways as a sum of one triangular number and 2 squares (each of them >= 0).

%e a(4)=10 since 10 can be expressed in 4 ways,

%e 10=T(4)+0^2+0^2 = T(3)+0^2+2^2 = T(1)+0^2+3^2 = T(0)+1^2+3^2 and none of the numbers from 0 to 9 can be expressed in 4 ways.

%t V = Table[0, {i, 5000}]; T[n]:=n(n+1)/2; Do[a = T[i]+j^2+k^2; If[a<5000, V[[a+1]]++ ], {i, 0, 100}, {j, 0, 71}, {k, 0, j}]; Table[Position[V, z][[1, 1]]-1, {z, 60}]

%Y Cf. A115288, A000437, A061262.

%K nonn

%O 1,3

%A _Giovanni Resta_, Jan 19 2006