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Search: id:A129709
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| A129709 |
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Triangle read by rows: T(n,k) is the number of Fibonacci binary words of length n and having k 011 subwords (0<=k<=floor(n/3)). A Fibonacci binary word is a binary word having no 00 subword. |
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+0
1
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| 1, 2, 3, 4, 1, 5, 3, 6, 7, 7, 13, 1, 8, 22, 4, 9, 34, 12, 10, 50, 28, 1, 11, 70, 58, 5, 12, 95, 108, 18, 13, 125, 188, 50, 1, 14, 161, 308, 121, 6, 15, 203, 483, 261, 25, 16, 252, 728, 520, 80, 1, 17, 308, 1064, 968, 220, 7, 18, 372, 1512, 1710, 536, 33, 19, 444, 2100
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OFFSET
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0,2
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COMMENT
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Also number of Fibonacci binary words of length n and having k 110 subwords. Row n has 1+floor(n/3) terms. Row sums are the Fibonacci numbers (A000045). T(n,0)=n+1. Sum(k*T(n,k), k>=0)=A023610(n-3).
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FORMULA
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G.f.=G(t,z)=(1+z)/(1-z-z^2+z^3-tz^3).
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EXAMPLE
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T(7,2)=4 because we have 1011011,0111011,0110110, and 0110111.
Triangle starts:
1;
2;
3;
4,1;
5,3;
6,7;
7,13,1;
8,22,4;
9,34,12;
10,50,28,1;
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MAPLE
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G:=(1+z)/(1-z-z^2+z^3-t*z^3): Gser:=simplify(series(G, z=0, 23)): for n from 0 to 20 do P[n]:=sort(coeff(Gser, z, n)) od: for n from 0 to 20 do seq(coeff(P[n], t, j), j=0..floor(n/3)) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000045, A023610.
Adjacent sequences: A129706 A129707 A129708 this_sequence A129710 A129711 A129712
Sequence in context: A026280 A115994 A071437 this_sequence A133108 A055441 A104717
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KEYWORD
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nonn,tabf
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), May 12 2007
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