A083656 a(n) = Sum_{i=1..n} floor(r*floor(r*i)), where r=sqrt(2).
1, 3, 8, 15, 24, 35, 47, 62, 78, 97, 118, 140, 165, 191, 220, 251, 284, 319, 355, 394, 435, 478, 523, 569, 618, 668, 721, 776, 833, 892, 952, 1015, 1080, 1147, 1216, 1286, 1359, 1433, 1510, 1589, 1669, 1752, 1836, 1923, 2012, 2103, 2196, 2290, 2387, 2485, 2586
Offset: 1
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 1..5000
Programs
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Magma
[(&+[Floor(Sqrt(2)*Floor(Sqrt(2)*j)): j in [1..n]]): n in [1..60]]; // G. C. Greubel, Oct 01 2018
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Mathematica
Table[Sum[Floor[Sqrt[2]Floor[Sqrt[2]x]],{x,n}],{n,60}] (* Harvey P. Dale, Jul 20 2018 *) -
PARI
a(n) = sum(i=1, n, floor(sqrt(2)*floor(sqrt(2)*i))); \\ Michel Marcus, Dec 05 2013
Formula
a(n) = n*(n-1+1/sqrt(2)) + O(1).
Comments