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%I #9 Feb 26 2014 00:55:44
%S 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 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 10,12,11,8,9,11,11,10,8,9,10,7,9,13,12
%N a(n)=sum{k=0..n, mod(C(floor(k/2),n-k),2)}.
%C Row sums of number triangle A127829.
%C From _Johannes W. Meijer_, Jun 05 2011: (Start)
%C The Ze3 and Ze4 triangle sums, see A180662 for their definitions, of Sierpinski's triangle A047999 equal this sequence.
%C 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 a(2^n)=F(n); a(2^(n+1)+1)=L(n); a(n) mod 2=A000931(n+5) mod 2=A011656(n+4).
%p 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
%Y 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 easy,nonn
%O 0,4
%A _Paul Barry_, Feb 01 2007
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