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A120924
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Triangle read by rows: T(n,k) is the number of ternary words of length n on {0,1,2}, having k isolated 0's (n>=0, k>=0).
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2
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1, 2, 1, 5, 4, 13, 12, 2, 33, 36, 12, 83, 108, 48, 4, 209, 316, 172, 32, 527, 904, 588, 160, 8, 1329, 2548, 1932, 672, 80, 3351, 7104, 6140, 2592, 480, 16, 8449, 19628, 19020, 9440, 2320, 192, 21303, 53816, 57756, 32896, 10000, 1344, 32, 53713, 146596
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row n has 1+ceil(n/2) terms. Row sums are the powers of 3 (A000244). T(n,0)=A120925(n). Sum(k*T(n,k),k=0..ceil(n/2))=A120926(n)
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FORMULA
| G.f.=G(t,z)=[1-(1-t)z(1-z)]/[1-3z+2(1-t)z^2*(1-z)].
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EXAMPLE
| T(2,0)=5 because we have 00,11,12,21 and 22; T(2,1)=4 because we have 01,02,10 and 20; T(3,2)=2 because we have 010 and 020.
Triangle starts:
1;
2,1;
5,4;
13,12,2;
33,36,12;
83,108,48,4;
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MAPLE
| G:=(1-(1-t)*z*(1-z))/(1-3*z+2*(1-t)*z^2*(1-z)): Gser:=simplify(series(G, z=0, 15)): P[0]:=1: for n from 1 to 13 do P[n]:=sort(coeff(Gser, z^n)) od: for n from 0 to 13 do seq(coeff(P[n], t, j), j=0..ceil(n/2)) od; # yields sequence in triangular form
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CROSSREFS
| Cf. A000244, A105114, A120925, A120926.
Sequence in context: A144240 A119914 A152192 * A079285 A124660 A141485
Adjacent sequences: A120921 A120922 A120923 * A120925 A120926 A120927
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KEYWORD
| nonn,tabf
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 16 2006
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