This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A255773 #20 Jun 01 2022 12:16:18
%S A255773 1,3,4,6,8,9,12,11,14,16,21,17,22,25,33,19,24,27,35,29,37,42,55,30,38,
%T A255773 43,56,46,59,67,88,32,40,45,58,48,61,69,90,50,63,71,92,76,97,110,144,
%U A255773 51,64,72,93,77,98,111,145,80,101,114,148,122,156,177,232
%N A255773 Tree of lower Wythoff numbers (A000201) generated as the 1-component of the graph described at A095903.
%C A255773 This sequence and A255774 partition the positive integers.
%e A255773 To generate the tree of lazy Fibonacci representations as in A095903, start with 1,2. Suffix the next two Fibonacci numbers, getting 1+2, 1+3; 2+3, 2+5. Suffix the next two Fibonacci numbers, getting 1+2+3, 1+2+5, 1+3+5, 1+3+8; 2+3+5, 2+3+8, 2+5+8, 2+5+13. Continue forever. A255773 is the tree of numbers having root (initial summand) 1, and A255774 is the tree of numbers having root (initial summand) 2.
%t A255773 width = 6;t = Map[Total, Fibonacci[Flatten[NestList[Flatten[Map[{Join[#, {Last[#] +1}], Join[#, {Last[#] + 2}]} &, #], 1] &, {{2}, {3}}, width], 1]]](*A095903*)
%t A255773 Map[t[[#]] &, Apply[Range, {2^Range[#] - 1, 3 2^(Range[#] - 1) - 2}]] &[width + 1] (*A255773*)
%t A255773 Map[t[[#]] &,Apply[Range, {3 2^(Range[#] - 1) - 1, 2 (2^Range[#] - 1)}]] &[width + 1] (*A255774*) (* _Peter J. C. Moses_, Mar 06 2015 *)
%Y A255773 Cf. A000201, A095903, A244774.
%K A255773 nonn,easy
%O A255773 1,2
%A A255773 _Clark Kimberling_, Mar 06 2015