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A165453

Linear interpolation of the sequence that maps an entry of A002378 to the corresponding entry of A006331.

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

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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

a(n) = A022554(n) + A080344(n). - Ridouane Oudra, Sep 29 2025

MATHEMATICA

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