A293688 Partial sums of A002251.

0, 2, 3, 8, 15, 18, 28, 32, 45, 60, 66, 84, 104, 112, 135, 144, 170, 198, 209, 240, 252, 286, 322, 336, 375, 416, 432, 476, 493, 540, 589, 608, 660, 714, 735, 792, 814, 874, 936, 960, 1025, 1050, 1118, 1188, 1215, 1288, 1363, 1392, 1470, 1500, 1581, 1664, 1696, 1782, 1815

Offset: 0

Author

Enrique Navarrete, Oct 14 2017

Keywords

• nonn

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A002251, A005206.

Programs

Mathematica

With[{n = 34}, Accumulate@ Prepend[Take[Values@ #, LengthWhile[#, # == 1 &] &@ Differences@ Keys@ #], 0] &@ Sort@ Flatten@ Map[{#1 -> #2, #2 -> #1} & @@ # &, Transpose@ {Array[Floor[# GoldenRatio] &, n], Array[Floor[# GoldenRatio^2] &, n]}]] (* Michael De Vlieger, Nov 14 2017 *)

Formula

a(n) = (n+1)*A005206(n) where A005206 is the Hofstadter G-sequence. [Apparently this is a conjecture, rather than a theorem. - N. J. A. Sloane, Mar 03 2019]

a(n) = Sum_{k=0..n} A002251(k). - Michel Marcus, Nov 13 2017

Extensions

Offset changed to 0 by Michel Marcus, Nov 13 2017