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 A127830 #20 Jul 30 2025 01:01:03
%S A127830 1,1,1,2,2,1,2,3,3,3,2,2,3,2,3,5,5,4,4,5,4,3,3,3,4,4,3,4,5,3,5,8,8,7,
%T A127830 6,7,7,5,6,8,7,6,5,5,5,4,4,5,6,5,5,7,6,4,5,6,7,7,5,6,8,5,8,13,13,11,
%U A127830 10,12,11,8,9,11,11,10,8,9,10,7,9,13,12
%N A127830 a(n) = Sum_{k=0..n} (binomial(floor(k/2),n-k) mod 2).
%C A127830 Row sums of number triangle A127829.
%C A127830 From _Johannes W. Meijer_, Jun 05 2011: (Start)
%C A127830 The Ze3 and Ze4 triangle sums, see A180662 for their definitions, of Sierpinski's triangle A047999 equal this sequence.
%C A127830 The sequences A127830(2^n-p), p>=0, are apparently all Fibonacci like sequences, i.e., the next term is the sum of the two nonzero terms that precede it; see the crossrefs. (End)
%F A127830 a(2^n) = F(n); a(2^(n+1)+1) = L(n).
%F A127830 a(n) mod 2 = A000931(n+5) mod 2 = A011656(n+4).
%p A127830 A127830 := proc(n) local k: option remember: add(binomial(floor(k/2), n-k) mod 2, k=0..n) end: seq(A127830(n), n=0..80); # _Johannes W. Meijer_, Jun 05 2011
%t A127830 Table[Sum[Mod[Binomial[Floor[k/2],n-k],2],{k,0,n}],{n,0,80}] (* _James C. McMahon_, Jan 04 2025 *)
%o A127830 (Python)
%o A127830 def A127830(n): return sum(not ~(k>>1)&n-k for k in range(n+1)) # _Chai Wah Wu_, Jul 29 2025
%Y A127830 Cf.: A000045 (p=0), A000204 (p=7), A001060 (p=13), A000285 (p=14), A022095 (p=16), A022120 (p=24), A022121 (p=25), A022113 (p=28), A022096 (p=30), A022097 (p=31), A022098 (p=32), A022130 (p=44), A022137 (p=48), A022138 (p=49), A022122 (p=52), A022114 (p=53), A022123 (p=56), A022115 (p=60), A022100 (p=62), A022101 (p=63), A022103 (p=64), A022136 (p=79), A022388 (p=80), A022389 (p=88). - _Johannes W. Meijer_, Jun 05 2011
%K A127830 easy,nonn
%O A127830 0,4
%A A127830 _Paul Barry_, Feb 01 2007