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A276797
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Partial sums of A276794.
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11
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0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 23, 23, 23, 23, 24, 24, 25
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OFFSET
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0,7
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COMMENTS
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a(n+1) = z_A(n), the number of entries of A278040 (called A number in the W. Lang given there) not exceeding n, for n >= 1 and z_A(-1) := 0. - Wolfdieter Lang, Dec 06 2018
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LINKS
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FORMULA
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a(n) = 2*B(n) - A(n) + 1, for n >= 0, where A(n) = A278040(n) and B(n) = A278039(n). For a proof see the W. Lang link in A278040, Proposition 7, eq. (41). - Wolfdieter Lang, Dec 06 2018
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MAPLE
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M:=12;
S[1]:=`0`; S[2]:=`01`; S[3]:=`0102`;
for n from 4 to M do S[n]:=cat(S[n-1], S[n-2], S[n-3]); od:
t0:=S[M]: # has 927 terms of tribonacci ternary word A080843
# get numbers of 0's, 1's, 2's
N0:=[]: N1:=[]: N2:=[]: c0:=0: c1:=0: c2:=0:
L:=length(t0);
for i from 1 to L do
js := substring(t0, i..i);
j:=convert(js, decimal, 10);
if j=0 then c0:=c0+1; elif j=1 then c1:=c1+1; else c2:=c2+1; fi;
N0:=[op(N0), c0]; N1:=[op(N1), c1]; N2:=[op(N2), c2];
od:
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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