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 A127830 a(n)=sum{k=0..n, mod(C(floor(k/2),n-k),2)}. 3
 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, 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, 10, 12, 11, 8, 9, 11, 11, 10, 8, 9, 10, 7, 9, 13, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Row sums of number triangle A127829. From Johannes W. Meijer, Jun 05 2011: (Start) The Ze3 and Ze4 triangle sums, see A180662 for their definitions, of Sierpinski's triangle A047999 equal this sequence. 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) LINKS FORMULA a(2^n)=F(n); a(2^(n+1)+1)=L(n); a(n) mod 2=A000931(n+5) mod 2=A011656(n+4). MAPLE 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 CROSSREFS 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 Sequence in context: A029257 A194258 A165927 * A176816 A053284 A050371 Adjacent sequences:  A127827 A127828 A127829 * A127831 A127832 A127833 KEYWORD easy,nonn AUTHOR Paul Barry, Feb 01 2007 STATUS approved

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Last modified September 23 08:04 EDT 2021. Contains 347610 sequences. (Running on oeis4.)