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A118890 Triangle read by rows: T(n,k) is the number of binary sequences of length n containing k subsequences 0110 (n,k>=0). 4
1, 2, 4, 8, 15, 1, 28, 4, 52, 12, 97, 30, 1, 181, 70, 5, 338, 156, 18, 631, 339, 53, 1, 1178, 722, 142, 6, 2199, 1515, 357, 25, 4105, 3140, 862, 84, 1, 7663, 6444, 2018, 252, 7, 14305, 13116, 4614, 700, 33, 26704, 26513, 10348, 1846, 124, 1, 49850, 53280, 22844 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row n has ceil(n/3) terms (n>=1). Sum of entries in row n is 2^n (A000079). T(n,0) = A049864(n). T(n,1) = A118892(n). Sum(k*T(n,k), n>=0) = (n-3)*2^(n-4) (A001787).

LINKS

Alois P. Heinz, Rows n = 0..250, flattened

FORMULA

G.f.: G(t,z) = [1+(1-t)z^3]/[1-2z+(1-t)(1-z)z^3].

EXAMPLE

T(8,2) = 5 because we have 01100110, 01101100, 01101101, 00110110 and 10110110.

Triangle starts:

1;

2;

4;

8;

15,  1;

28,  4;

52,  12;

97,  30,  1;

181, 70,  5;

338, 156, 18;

631, 339, 53, 1;

MAPLE

G:=(1+(1-t)*z^3)/(1-2*z+(1-t)*(1-z)*z^3): Gser:=simplify(series(G, z=0, 24)): P[0]:=1: for n from 1 to 18 do P[n]:=sort(coeff(Gser, z^n)) od: 1; for n from 1 to 18 do seq(coeff(P[n], t, j), j=0..ceil(n/3)-1) od; # yields sequence in triangular form

MATHEMATICA

nn=12; c=x^3; Map[Select[#, #>0&]&, CoefficientList[Series[1/(1-2x - (y-1)x^4/ (1-(y-1)c)), {x, 0, nn}], {x, y}]]//Grid (* Geoffrey Critzer, Dec 25 2013 *)

CROSSREFS

Cf. A000079, A049864, A118892, A011787.

Sequence in context: A028398 A155249 A118884 * A118869 A118897 A098056

Adjacent sequences:  A118887 A118888 A118889 * A118891 A118892 A118893

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, May 04 2006

STATUS

approved

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Last modified October 22 06:02 EDT 2018. Contains 316432 sequences. (Running on oeis4.)