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%I #15 Jun 11 2024 13:03:01
%S 1,3,7,10,19,24,40,46,71,78,114,122,171,181,245,256,337,349,449,462,
%T 583,597,741,756,925,942,1138,1156,1381,1400,1656,1676,1965,1986,2310,
%U 2332,2693,2716,3116,3140,3581,3607,4091,4118,4647,4675,5251,5280,5905,5935
%N Partial sums of A137442.
%H Gerald Hillier, <a href="/A167390/b167390.txt">Table of n, a(n) for n = 1..1000</a>
%F Set R(N)=N+ROUND(SQRT(N),0), S(N)=FLOOR(SQRT(R(N))), U(N)=R(N)*(R(N)+1)/2-S(N)*(S(N)+1)*(S(N)+.5)/3, T(N)=CEILING(N/2), then a(N)=T(N)*(1+T(N)*(3+2*T(N)))/6+U(FLOOR(N/2))
%e a(14)=1+2+4+3+9+5+16+6+25+7+36+8+49+10=181
%t Module[{nn=40,sq,int,len},sq=Range[nn]^2;int=Complement[Range[nn],sq];len=Min[ Length[ int],nn]; Riffle[Take[ sq,len],Take[ int,len]]]//Accumulate (* _Harvey P. Dale_, Jun 11 2024 *)
%K nonn
%O 1,2
%A _Gerald Hillier_, Nov 02 2009
%E Terms a(15) and above from _Gerald Hillier_, Jan 06 2022