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A083656 a(n) = Sum_{i=1..n} floor(r*floor(r*i)), where r=sqrt(2).

%I A083656 #15 Sep 08 2022 08:45:10
%S A083656 1,3,8,15,24,35,47,62,78,97,118,140,165,191,220,251,284,319,355,394,
%T A083656 435,478,523,569,618,668,721,776,833,892,952,1015,1080,1147,1216,1286,
%U A083656 1359,1433,1510,1589,1669,1752,1836,1923,2012,2103,2196,2290,2387,2485,2586
%N A083656 a(n) = Sum_{i=1..n} floor(r*floor(r*i)), where r=sqrt(2).
%C A083656 Partial sums of A007069.
%H A083656 G. C. Greubel, <a href="/A083656/b083656.txt">Table of n, a(n) for n = 1..5000</a>
%F A083656 a(n) = n*(n-1+1/sqrt(2)) + O(1).
%t A083656 Table[Sum[Floor[Sqrt[2]Floor[Sqrt[2]x]],{x,n}],{n,60}] (* _Harvey P. Dale_, Jul 20 2018 *)
%o A083656 (PARI) a(n) = sum(i=1, n, floor(sqrt(2)*floor(sqrt(2)*i))); \\ _Michel Marcus_, Dec 05 2013
%o A083656 (Magma) [(&+[Floor(Sqrt(2)*Floor(Sqrt(2)*j)): j in [1..n]]): n in [1..60]]; // _G. C. Greubel_, Oct 01 2018
%K A083656 nonn
%O A083656 1,2
%A A083656 _Benoit Cloitre_, Jun 13 2003