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a(n) = Sum_{j=1..n} floor(j*sqrt(13)); n-th partial sum of Beatty sequence for sqrt(13).
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%I #10 Mar 17 2021 22:55:48

%S 3,10,20,34,52,73,98,126,158,194,233,276,322,372,426,483,544,608,676,

%T 748,823,902,984,1070,1160,1253,1350,1450,1554,1662,1773,1888,2006,

%U 2128,2254,2383,2516,2653,2793,2937,3084,3235,3390,3548,3710,3875

%N a(n) = Sum_{j=1..n} floor(j*sqrt(13)); n-th partial sum of Beatty sequence for sqrt(13).

%t c[n_] := Sum[Floor[j*Sqrt[13]], {j, 1, n}];

%t c = Table[c[n], {n, 1, 90}]

%o (Python)

%o from sympy import integer_nthroot

%o def A194116(n): return sum(integer_nthroot(13*j**2,2)[0] for j in range(1,n+1)) # _Chai Wah Wu_, Mar 17 2021

%Y Cf. A171983 (Beatty sequence for sqrt(13)).

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 16 2011