A167390 Partial sums of A137442.

1, 3, 7, 10, 19, 24, 40, 46, 71, 78, 114, 122, 171, 181, 245, 256, 337, 349, 449, 462, 583, 597, 741, 756, 925, 942, 1138, 1156, 1381, 1400, 1656, 1676, 1965, 1986, 2310, 2332, 2693, 2716, 3116, 3140, 3581, 3607, 4091, 4118, 4647, 4675, 5251, 5280, 5905, 5935

Offset: 1

Author

Gerald Hillier, Nov 02 2009

Keywords

• nonn

Examples

			a(14)=1+2+4+3+9+5+16+6+25+7+36+8+49+10=181
		

Links

• Gerald Hillier, Table of n, a(n) for n = 1..1000

Programs

Mathematica

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 *)

Formula

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))

Extensions

Terms a(15) and above from Gerald Hillier, Jan 06 2022