A293403 Greatest integer k such that k/n^2 < (3 + sqrt(5))/2.

0, 2, 10, 23, 41, 65, 94, 128, 167, 212, 261, 316, 376, 442, 513, 589, 670, 756, 848, 945, 1047, 1154, 1267, 1384, 1507, 1636, 1769, 1908, 2052, 2201, 2356, 2515, 2680, 2851, 3026, 3207, 3392, 3584, 3780, 3982, 4188, 4400, 4618, 4840, 5068, 5301, 5539, 5783

Offset

0,2

Links

Clark Kimberling, Table of n, a(n) for n = 0..1000

Formula

a(n) = floor(r*n^2), where r = (3 + sqrt(5))/2.

a(n) = A293404(n) - 1 for n > 0.

Mathematica

z = 120; r = 1+GoldenRatio;
Table[Floor[r*n^2], {n, 0, z}];   (* A293403 *)
Table[Ceiling[r*n^2], {n, 0, z}]; (* A293404 *)
Table[Round[r*n^2], {n, 0, z}];   (* A293405 *)

Crossrefs

Cf. A001622, A293401, A293404, A293405.

Sequence in context: A284360 A372846 A255606 * A316451 A120845 A373276

Adjacent sequences: A293400 A293401 A293402 * A293404 A293405 A293406

Keyword

nonn,easy

Author

Clark Kimberling, Oct 11 2017

Status

approved