A194148 Sum_{j=1..n} floor(j*(1/2 + sqrt(2))); n-th partial sum of Beatty sequence for 1/2 + sqrt(2).

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 143, 167, 193, 221, 251, 283, 317, 353, 391, 431, 473, 517, 562, 609, 658, 709, 762, 817, 874, 933, 994, 1057, 1122, 1188, 1256, 1326, 1398, 1472, 1548, 1626, 1706, 1788, 1872, 1958, 2046, 2135, 2226, 2319

Offset: 1

Author

Clark Kimberling, Aug 17 2011

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A137803 (Beatty sequence for 1/2 + sqrt(2)).

Programs

Magma

[(&+[Floor(k*(Sqrt(2) + 1/2)): k in [1..n]]): n in [1..60]]; // G. C. Greubel, Oct 05 2018

Mathematica

c[n_] := Sum[Floor[j*(1/2+Sqrt[2])], {j, 1, n}];
c = Table[c[n], {n, 1, 90}]
Accumulate[Table[Floor[n(1/2+Sqrt[2])],{n,50}]] (* Harvey P. Dale, May 26 2023 *)

PARI

for(n=1,60, print1(sum(j=1,n, floor(j*(sqrt(2) + 1/2))), ", ")) \\ G. C. Greubel, Oct 05 2018