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Search: id:A130136
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| A130136 |
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Triangle read by rows: T(n,k) is the number of Fibonacci binary words of length n and having k 0110's (n>=0, 0<=k<=floor((n-1)/3)). A Fibonacci binary word is a binary word having no 00 subword. |
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+0
2
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| 1, 2, 3, 5, 7, 1, 11, 2, 16, 5, 25, 8, 1, 37, 16, 2, 57, 26, 6, 85, 48, 10, 1, 130, 78, 23, 2, 195, 136, 39, 7, 297, 220, 80, 12, 1, 447, 371, 136, 31, 2, 679, 598, 258, 54, 8, 1024, 987, 437, 121, 14, 1, 1553, 1584, 790, 212, 40, 2, 2345, 2576, 1332, 432, 71, 9, 3553
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Row n has 1+floor((n-1)/3) terms. Row sums are the Fibonacci numbers (A000045). T(n,0)=A130137(n). Sum(k*T(n,k), k>=0)=A001629(n-2) (n>=2).
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FORMULA
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G.f.=G(t,z)=[1+z+(1-t)z^3]/[1-z-z^2+(1-t)z^3-(1-t)z^4].
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EXAMPLE
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T(8,2)=2 because we have 01101101 and 10110110.
Triangle starts:
1;
2;
3;
5;
7,1;
11,2;
16,5;
25,8,1;
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MAPLE
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G:=(1+z+z^3-t*z^3)/(1-z-z^2+z^3-t*z^3-z^4+t*z^4): Gser:=simplify(series(G, z=0, 23)): for n from 0 to 23 do P[n]:=sort(coeff(Gser, z, n)) od: 1; for n from 1 to 20 do seq(coeff(P[n], t, j), j=0..floor((n-1)/3)) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000045, A001629, A130137.
Sequence in context: A101987 A126052 A130138 this_sequence A032759 A142711 A093338
Adjacent sequences: A130133 A130134 A130135 this_sequence A130137 A130138 A130139
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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 13 2007
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