A194138 a(n) = Sum_{j=1..n} floor(j*(1+sqrt(2))), n-th partial sum of Beatty sequence for 1+sqrt(2).

2, 6, 13, 22, 34, 48, 64, 83, 104, 128, 154, 182, 213, 246, 282, 320, 361, 404, 449, 497, 547, 600, 655, 712, 772, 834, 899, 966, 1036, 1108, 1182, 1259, 1338, 1420, 1504, 1590, 1679, 1770, 1864, 1960, 2058, 2159, 2262, 2368, 2476, 2587, 2700, 2815

Offset

1,1

Links

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

Mathematica

c[n_] := Sum[Floor[j*(1+Sqrt[2])], {j, 1, n}];
c = Table[c[n], {n, 1, 90}]

Prog

(PARI) for(n=1, 60, print1(sum(j=1, n, floor(j*(1+sqrt(2)))), ", ")) \\ G. C. Greubel, Oct 05 2018
(Magma) [(&+[Floor(k*(1+Sqrt(2))): k in [1..n]]): n in [1..60]] // G. C. Greubel, Oct 05 2018

Crossrefs

Cf. A003151 (Beatty sequence for 1+sqrt(2)).

Sequence in context: A230537 A267874 A194143 * A194137 A226292 A026052

Adjacent sequences: A194135 A194136 A194137 * A194139 A194140 A194141

Keyword

nonn

Author

Clark Kimberling, Aug 17 2011

Status

approved