A129230 a(n) = floor(n*r) + floor((n-2)*r) + floor((n-4)*r) + ... + floor(k*r), where r = golden ratio = (1 + sqrt(5))/2 and k = n mod 2.

0, 1, 3, 5, 9, 13, 18, 24, 30, 38, 46, 55, 65, 76, 87, 100, 112, 127, 141, 157, 173, 190, 208, 227, 246, 267, 288, 310, 333, 356, 381, 406, 432, 459, 487, 515, 545, 574, 606, 637, 670, 703, 737, 772, 808, 844, 882, 920, 959, 999, 1039, 1081, 1123, 1166, 1210

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Formula

a(n) = Sum_{k=0..n} A129229(k).

Mathematica

Module[{nn=60, fgm}, fgm=Floor[GoldenRatio*Range[nn]]; Union[Flatten[ Table[ {Total[ Take[fgm, {1, n, 2}]], Total[Take[fgm, {2, n, 2}]]}, {n, nn}]]]] (* Harvey P. Dale, Feb 03 2016 *)
Accumulate[Block[{n = 0}, NestList[Floor[++n*GoldenRatio] - # &, 0, 100]]] (* Paolo Xausa, May 12 2024 *)

Crossrefs

Cf. A129229.

Sequence in context: A356254 A122248 A024403 * A203567 A350660 A071404

Adjacent sequences: A129227 A129228 A129229 * A129231 A129232 A129233

Keyword

nonn

Author

Clark Kimberling, Apr 04 2007

Status

approved