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A194113 a(n) = Sum_{j=1..n} floor(j*sqrt(10)); n-th partial sum of Beatty sequence for sqrt(10).

%I A194113 #38 Jul 23 2024 10:49:16
%S A194113 3,9,18,30,45,63,85,110,138,169,203,240,281,325,372,422,475,531,591,
%T A194113 654,720,789,861,936,1015,1097,1182,1270,1361,1455,1553,1654,1758,
%U A194113 1865,1975,2088,2205,2325,2448,2574,2703,2835,2970,3109,3251,3396,3544
%N A194113 a(n) = Sum_{j=1..n} floor(j*sqrt(10)); n-th partial sum of Beatty sequence for sqrt(10).
%C A194113 From _Marius A. Burtea_, Aug 22 2018: (Start)
%C A194113   a(2)      =            9 =      3^2;
%C A194113   a(10)     =          169 =     13^2;
%C A194113   a(76)     =         9216 =     96^2;
%C A194113   a(783)    =       970225 =    985^2;
%C A194113   a(5895)   =     54952569 =   7413^2;
%C A194113   a(187507) =  55591265284 = 235778^2;
%C A194113   a(577771) = 527815327081 = 726509^2;
%C A194113   ...
%C A194113 Does the sequence include an infinite number of perfect squares? (End)
%H A194113 G. C. Greubel, <a href="/A194113/b194113.txt">Table of n, a(n) for n = 1..1000</a>
%t A194113 Table[Sum[Floor[j*Sqrt[10]], {j, 1, n}], {n, 1, 90}]
%o A194113 (PARI) for(n=1,50, print1(sum(k=1,n, floor(k*sqrt(10))), ", ")) \\ _G. C. Greubel_, Sep 24 2017
%o A194113 (Python)
%o A194113 from math import isqrt
%o A194113 def A194113(n): return sum(isqrt(10*j**2) for j in range(1,n+1)) # _Chai Wah Wu_, Jul 23 2024
%Y A194113 Cf. A177102 (Beatty sequence for sqrt(10)).
%K A194113 nonn
%O A194113 1,1
%A A194113 _Clark Kimberling_, Aug 16 2011