login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A165453 Linear interpolation of the sequence that maps an entry of A002378 to the corresponding entry of A006331. 0
0, 1, 2, 4, 6, 8, 10, 13, 16, 19, 22, 25, 28, 32, 36, 40, 44, 48, 52, 56, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 116, 122, 128, 134, 140, 146, 152, 158, 164, 170, 176, 182, 189, 196, 203, 210, 217, 224, 231, 238, 245, 252, 259, 266, 273, 280, 288, 296, 304 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..59.

FORMULA

a(0)=0, a(n) = max(min(a(n-1)+x, n+a(n-x))), where the maximum is taken over all values for x from 1 to n.

a(n) = Sum_{k=1..n} floor(sqrt(k)+1/2). - Wesley Ivan Hurt, Dec 01 2020

a(n) = (1/3)*t*(3*n + 1 - t^2), where t = floor(sqrt(n)+1/2). - Ridouane Oudra, Feb 22 2021

MATHEMATICA

f[n_]:=Round[Sqrt[n]]; a=0; lst={}; Do[AppendTo[lst, a+=f[n]], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 13 2009 *)

Table[Sum[Floor[Sqrt[n + 1 - k] + 1/2], {k, n + 1}], {n, 0, 100}] (* Wesley Ivan Hurt, Dec 01 2020 *)

CROSSREFS

Cf. A002378, A006331.

Sequence in context: A130174 A061168 A130798 * A282168 A025224 A294023

Adjacent sequences:  A165450 A165451 A165452 * A165454 A165455 A165456

KEYWORD

easy,nonn

AUTHOR

Friedrich Regen (friedrich.regen(AT)tu-ilmenau.de), Sep 20 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 30 04:18 EDT 2021. Contains 346348 sequences. (Running on oeis4.)