login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Sum{floor(j*(3+sqrt(3))/2) : 1<=j<=n}; n-th partial sum of Beatty sequence for (3+sqrt(3))/2.
2

%I #9 Apr 18 2022 16:27:15

%S 2,6,13,22,33,47,63,81,102,125,151,179,209,242,277,314,354,396,440,

%T 487,536,588,642,698,757,818,881,947,1015,1085,1158,1233,1311,1391,

%U 1473,1558,1645,1734,1826,1920,2017,2116,2217,2321,2427,2535,2646,2759

%N Sum{floor(j*(3+sqrt(3))/2) : 1<=j<=n}; n-th partial sum of Beatty sequence for (3+sqrt(3))/2.

%H Harvey P. Dale, <a href="/A194143/b194143.txt">Table of n, a(n) for n = 1..1000</a>

%t c[n_] := Sum[Floor[j*(3+Sqrt[3])/2], {j, 1, n}];

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

%t Accumulate[Floor[(3+Sqrt[3])/2 Range[50]]] (* _Harvey P. Dale_, Apr 18 2022 *)

%Y Cf. A054406 (Beatty sequence for (3+sqrt(3))/2).

%K nonn

%O 1,1

%A _Clark Kimberling_, Aug 17 2011