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%I #15 May 26 2023 13:56:00
%S 1,4,9,16,25,36,49,64,81,100,121,143,167,193,221,251,283,317,353,391,
%T 431,473,517,562,609,658,709,762,817,874,933,994,1057,1122,1188,1256,
%U 1326,1398,1472,1548,1626,1706,1788,1872,1958,2046,2135,2226,2319
%N Sum_{j=1..n} floor(j*(1/2 + sqrt(2))); n-th partial sum of Beatty sequence for 1/2 + sqrt(2).
%H G. C. Greubel, <a href="/A194148/b194148.txt">Table of n, a(n) for n = 1..5000</a>
%t c[n_] := Sum[Floor[j*(1/2+Sqrt[2])], {j, 1, n}];
%t c = Table[c[n], {n, 1, 90}]
%t Accumulate[Table[Floor[n(1/2+Sqrt[2])],{n,50}]] (* _Harvey P. Dale_, May 26 2023 *)
%o (PARI) for(n=1,60, print1(sum(j=1,n, floor(j*(sqrt(2) + 1/2))), ", ")) \\ _G. C. Greubel_, Oct 05 2018
%o (Magma) [(&+[Floor(k*(Sqrt(2) + 1/2)): k in [1..n]]): n in [1..60]]; // _G. C. Greubel_, Oct 05 2018
%Y Cf. A137803 (Beatty sequence for 1/2 + sqrt(2)).
%K nonn
%O 1,2
%A _Clark Kimberling_, Aug 17 2011
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