A194139 a(n) = Sum_{j=1..n} floor(j*(2+sqrt(2))); n-th partial sum of Beatty sequence for 2+sqrt(2).

3, 9, 19, 32, 49, 69, 92, 119, 149, 183, 220, 260, 304, 351, 402, 456, 514, 575, 639, 707, 778, 853, 931, 1012, 1097, 1185, 1277, 1372, 1471, 1573, 1678, 1787, 1899, 2015, 2134, 2256, 2382, 2511, 2644, 2780, 2919, 3062, 3208, 3358, 3511, 3668

Offset

0,1

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

Mathematica

c[n_] := Sum[Floor[j*(2+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*(2+sqrt(2)))), ", ")) \\ G. C. Greubel, Oct 05 2018
(Magma) [(&+[Floor(k*(2+Sqrt(2))): k in [1..n]]): n in [1..60]] // G. C. Greubel, Oct 05 2018

Crossrefs

Cf. A001952 (Beatty sequence for 2+sqrt(2)).

Sequence in context: A350978 A143056 A294401 * A194115 A226184 A066506

Adjacent sequences: A194136 A194137 A194138 * A194140 A194141 A194142

Keyword

nonn

Author

Clark Kimberling, Aug 17 2011

Status

approved