A194117 a(n) = Sum_{j=1..n} floor(j*(1+sqrt(3))/2); n-th partial sum of Beatty sequence A003511.

1, 3, 7, 12, 18, 26, 35, 45, 57, 70, 85, 101, 118, 137, 157, 178, 201, 225, 250, 277, 305, 335, 366, 398, 432, 467, 503, 541, 580, 620, 662, 705, 750, 796, 843, 892, 942, 993, 1046, 1100, 1156, 1213, 1271, 1331, 1392, 1454, 1518, 1583, 1649, 1717

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Mathematica

a[n_] := Sum[Floor[j*(1+Sqrt[3])/2], {j, 1, n}]; Table[a[n], {n, 1, 90}]
With[{c=(1+Sqrt[3])/2}, Accumulate[Floor[c*Range[50]]]] (* Harvey P. Dale, Aug 02 2012 *)

Crossrefs

Cf. A003511 (Beatty sequence for (1+sqrt(3))/2).

Sequence in context: A257944 A005228 A000969 * A122250 A169679 A024388

Adjacent sequences: A194114 A194115 A194116 * A194118 A194119 A194120

Keyword

nonn

Author

Clark Kimberling, Aug 16 2011

Extensions

Definition corrected by Georg Fischer, Jul 31 2023

Status

approved