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%I #13 Apr 15 2020 15:09:41
%S 23,44,54,63,117,138,149,162,180,188,243,251,261,270,287,294,398,401,
%T 458,512,611,657,684,693,734,797,842,863,914,932,936,945,987,1029,
%U 1047,1098,1323,1401,1449,1472,1484,1494,1574,1608,1637,1769,1792,1799,1823,1839,1902,1995
%N Positive numbers not of the form 4*x^4 + y*(y+1)/2 + z*(z+1)/2, where x,y,z are nonnegative integers.
%C Conjecture: The sequence only has 602 terms as listed in the b-file.
%C Our computation indicates that after the 602-th term 31737789 there are no other terms below 10^8.
%C It is known that each n = 0,1,2,... can be written as the sum of an even square and two triangular numbers.
%H Zhi-Wei Sun, <a href="/A334113/b334113.txt">Table of n, a(n) for n = 1..602</a>
%H Zhi-Wei Sun, <a href="http://dx.doi.org/10.4064/aa127-2-1">Mixed sums of squares and triangular numbers</a>, Acta Arith. 127(2007), 103-113.
%t TQ[n_]:=TQ[n]=IntegerQ[Sqrt[8n+1]];
%t tab={};Do[Do[If[TQ[n-4x^4-y(y+1)/2],Goto[aa]],{x,0,(n/4)^(1/4)},{y,0,(Sqrt[4(n-4x^4)+1]-1)/2}];tab=Append[tab,n];Label[aa],{n,0,2000}];Print[tab]
%Y Cf. A000217, A000583, A115160, A306227, A334086.
%K nonn
%O 1,1
%A _Zhi-Wei Sun_, Apr 14 2020