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Search: id:A118890
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| A118890 |
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Triangle read by rows: T(n,k) is the number of binary sequences of length n containing k subsequences 0110 (n,k>=0). |
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+0
3
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| 1, 2, 4, 8, 15, 1, 28, 4, 52, 12, 97, 30, 1, 181, 70, 5, 338, 156, 18, 631, 339, 53, 1, 1178, 722, 142, 6, 2199, 1515, 357, 25, 4105, 3140, 862, 84, 1, 7663, 6444, 2018, 252, 7, 14305, 13116, 4614, 700, 33, 26704, 26513, 10348, 1846, 124, 1, 49850, 53280, 22844
(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 ceil(n/3) terms (n>=1). Sum of entries in row n is 2^n (A000079). T(n,0)=A049864(n). T(n,1)=A118892(n). Sum(k*T(n,k),n>=0)=(n-3)*2^(n-4) (A001787).
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FORMULA
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G.f.=G(t,z)=[1+(1-t)z^3]/[1-2z+(1-t)(1-z)z^3].
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EXAMPLE
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T(8,2)=5 because we have 01100110,01101100,01101101,00110110, and 10110110.
Triangle starts:
1;
2;
4;
8;
15,1;
28,4;
52,12;
97,30,1;
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MAPLE
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G:=(1+(1-t)*z^3)/(1-2*z+(1-t)*(1-z)*z^3): Gser:=simplify(series(G, z=0, 24)): P[0]:=1: for n from 1 to 18 do P[n]:=sort(coeff(Gser, z^n)) od: 1; for n from 1 to 18 do seq(coeff(P[n], t, j), j=0..ceil(n/3)-1) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000079, A049864, A118892, A011787.
Sequence in context: A093483 A028398 A118884 this_sequence A118869 A118897 A098056
Adjacent sequences: A118887 A118888 A118889 this_sequence A118891 A118892 A118893
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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 04 2006
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