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 A181631 #22 May 31 2025 06:48:58
%S A181631 1,1,2,1,2,3,1,1,2,3,4,1,1,1,2,2,3,4,5,1,1,1,1,1,2,2,2,3,3,4,5,6,1,1,
%T A181631 1,1,1,1,1,1,2,2,2,2,2,3,3,3,4,4,5,6,7,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,
%U A181631 2,2,2,2,2,2,3,3,3,3,3,4,4,4,5,5,6,7,8
%N A181631 Triangle by rows, number of leading 1's in the maximal Fibonacci representation (A104326).
%C A181631 Row sums = A001911: (1, 3, 6, 11, 19, 32, ...).
%C A181631 A112310 = number of 1's in the maximal Fibonacci representation, which has headings of (..., 8, 5, 3, 2, 1) filling entries from the right to left; as opposed to the minimal Fibonacci representation (A014417) which starts from the left. For example, 8 in maximal = 1011 = (5 + 2 + 1) whereas in minimal = (10000) = (8).
%C A181631 Rows have (1, 2, 3, 5, 8, ...) terms.
%H A181631 Amiram Eldar, <a href="/A181631/b181631.txt">Table of n, a(n) for n = 1..10000</a>
%F A181631 a(n) = A090996(A003754(n+1)). - _Amiram Eldar_, May 31 2025
%e A181631 First few rows of the triangle:
%e A181631 1;
%e A181631 1, 2;
%e A181631 1, 2, 3;
%e A181631 1, 1, 2, 3, 4;
%e A181631 1, 1, 1, 2, 2, 3, 4, 5;
%e A181631 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 6;
%e A181631 ...
%e A181631 Example: a(14) = 1 since 14 in the maximal Fibonacci representation is 10111.
%t A181631 f[s_] := Module[{i = FirstPosition[s, 0]}, If[MissingQ[i], Length[s], i[[1]] - 1]]; f /@ Select[IntegerDigits[#, 2] & /@ Range[300], SequencePosition[#, {0, 0}] == {} &] (* _Amiram Eldar_, May 31 2025 *)
%Y A181631 Cf. A000045 (row lengths), A003754, A001911 (row sums), A014417, A090996, A104326, A112310.
%K A181631 nonn,tabf
%O A181631 1,3
%A A181631 _Gary W. Adamson_, Nov 02 2010
%E A181631 More terms from _Amiram Eldar_, May 31 2025