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 A181371 Triangle read by rows: T(n,k) is the number of ternary words (i.e., finite sequences of 0's, 1's and 2's) of length n having k occurrences of 01's (0 <= k <= floor(n/2)). 1
 1, 3, 8, 1, 21, 6, 55, 25, 1, 144, 90, 9, 377, 300, 51, 1, 987, 954, 234, 12, 2584, 2939, 951, 86, 1, 6765, 8850, 3573, 480, 15, 17711, 26195, 12707, 2305, 130, 1, 46368, 76500, 43398, 10008, 855, 18, 121393, 221016, 143682, 40426, 4740, 183, 1, 317811 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row n contains 1 + floor(n/2) entries. Sum of entries in row n is 3^n = A000244(n). T(n,0) = F(2n+2) = A001906(n+1) (even-subscripted Fibonacci numbers). T(n,1) = A001871(n-2). Sum_{k>=0}k*T(n,k) = (n-1)*3^(n-2) = A027471(n) (n>=1). LINKS Alois P. Heinz, Rows n = 0..200, flattened Marilena Barnabei, Flavio Bonetti, and NiccolĂ˛ Castronuovo, Motzkin and Catalan Tunnel Polynomials, J. Int. Seq., Vol. 21 (2018), Article 18.8.8. FORMULA G.f. = G(t,z) = 1/(1 - 3z + z^2 - tz^2). EXAMPLE T(3,1)=6 because we have 010, 011, 012, 001, 101 and 201. T(4,2)=1 because we have 0101. Triangle starts:     1;     3;     8,  1;    21,  6;    55, 25,  1;   144, 90,  9; MAPLE G := 1/(1-3*z+z^2-t*z^2): Gser := simplify(series(G, z = 0, 15)): for n from 0 to 13 do P[n] := sort(coeff(Gser, z, n)) end do: for n from 0 to 13 do seq(coeff(P[n], t, k), k = 0 .. floor((1/2)*n)) end do; # yields sequence in triangular form CROSSREFS Cf. A000244, A001871, A001906, A027471. Sequence in context: A197725 A288875 A152230 * A118357 A278866 A281287 Adjacent sequences:  A181368 A181369 A181370 * A181372 A181373 A181374 KEYWORD nonn,tabf AUTHOR Emeric Deutsch, Oct 31 2010 STATUS approved

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Last modified June 21 05:34 EDT 2021. Contains 345355 sequences. (Running on oeis4.)