A167390 - OEIS

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

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OFFSET

1,2

LINKS

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

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))

EXAMPLE

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

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 *)

CROSSREFS

Sequence in context: A365931 A024330 A069153 * A000223 A366044 A031328

Adjacent sequences: A167387 A167388 A167389 * A167391 A167392 A167393

KEYWORD

nonn

AUTHOR

Gerald Hillier, Nov 02 2009

EXTENSIONS

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

STATUS

approved