

A128235


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<=n1).


3



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
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OFFSET

0,2


COMMENTS

Row n has n terms (n>=1). T(n,0) = A125145(n). Sum(k*T(n,k), k=0..n1) = (n1)*4^(n2) = A002697(n1).


LINKS



FORMULA

G.f.: (1+ztz)/(13z3z^2tz+3tz^2).


EXAMPLE

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;


MAPLE

G:=(1+zt*z)/(13*z3*z^2t*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..n1) od; # yields sequence in triangular form


CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



