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Search: id:A128235
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| A128235 |
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Triangle read by rows: T(n,k) is the number of sequences of length n on the alphabet {0,1,2,3}, containing k subsequences 00 (0<=k<=n-1). |
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+0
3
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| 1, 4, 15, 1, 57, 6, 1, 216, 33, 6, 1, 819, 162, 36, 6, 1, 3105, 756, 189, 39, 6, 1, 11772, 3402, 945, 216, 42, 6, 1, 44631, 14931, 4536, 1143, 243, 45, 6, 1, 169209, 64314, 21168, 5778, 1350, 270, 48, 6, 1, 641520, 273051, 96633, 28323, 7128, 1566, 297, 51
(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 n terms (n>=1). T(n,0)=A125145(n). Sum(k*T(n,k),k=0..n-1)=(n-1)*4^(n-2)=A002697(n-1).
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FORMULA
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G.f.=(1+z-tz)/(1-3z-3z^2-tz+3tz^2).
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EXAMPLE
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T(4,2)=6 because we have 0001,0002,0003,1000,2000, and 3000.
Triangle starts:
1;
4;
15,1;
57,6,1;
216,33,6,1;
819,162,36,6,1;
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MAPLE
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G:=(1+z-t*z)/(1-3*z-3*z^2-t*z+3*t*z^2): Gser:=simplify(series(G, z=0, 14)): for n from 0 to 11 do P[n]:=sort(coeff(Gser, z, n)) od: 1; for n from 1 to 11 do seq(coeff(P[n], t, j), j=0..n-1) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A125145, A002697.
Sequence in context: A022508 A097548 A127910 this_sequence A024547 A126601 A095331
Adjacent sequences: A128232 A128233 A128234 this_sequence A128236 A128237 A128238
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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), Feb 27 2007
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