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a(n) = floor(sqrt(2*n^3)).
2

%I #11 Sep 08 2022 08:45:50

%S 0,1,4,7,11,15,20,26,32,38,44,51,58,66,74,82,90,99,108,117,126,136,

%T 145,155,166,176,187,198,209,220,232,244,256,268,280,292,305,318,331,

%U 344,357,371,384,398,412,426,441,455,470,485,500,515,530,545,561,576,592

%N a(n) = floor(sqrt(2*n^3)).

%H Vincenzo Librandi, <a href="/A172472/b172472.txt">Table of n, a(n) for n = 0..1000</a>

%t Table[Floor[Sqrt[2 n^3]], {n, 0, 60}] (* _Vincenzo Librandi_, Aug 20 2014 *)

%o (Magma) [Floor(Sqrt(2*n^3)): n in [0..60]]; // _Vincenzo Librandi_, Aug 20 2014

%o (PARI) vector(100, n, n--; floor(sqrt(2*n^3))) \\ _G. C. Greubel_, Aug 18 2018

%K nonn

%O 0,3

%A _Vincenzo Librandi_, Feb 04 2010