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 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<=n-1). 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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). LINKS Alois P. Heinz, Rows n = 0..150, flattened FORMULA G.f.: (1+z-tz)/(1-3z-3z^2-tz+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+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 CROSSREFS Cf. A125145, A002697. Sequence in context: A218047 A344938 A261711 * A357116 A024547 A328839 Adjacent sequences: A128232 A128233 A128234 * A128236 A128237 A128238 KEYWORD nonn,tabf AUTHOR Emeric Deutsch, Feb 27 2007 STATUS approved

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Last modified December 7 08:09 EST 2023. Contains 367630 sequences. (Running on oeis4.)