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A118884 Triangle read by rows: T(n,k) is the number of binary sequences of length n containing k subsequences 0011 (n,k>=0). 3
1, 2, 4, 8, 15, 1, 28, 4, 52, 12, 96, 32, 177, 78, 1, 326, 180, 6, 600, 400, 24, 1104, 864, 80, 2031, 1827, 237, 1, 3736, 3800, 648, 8, 6872, 7800, 1672, 40, 12640, 15840, 4128, 160, 23249, 31884, 9846, 556, 1, 42762, 63704, 22844, 1752, 10, 78652, 126480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row n has 1+floor(n/4) terms. Sum of entries in row n is 2^n (A000079). T(n,0) = A008937(n+1). T(n,1) = A118885(n). Sum(k*T(n,k), k=0..n-1) = (n-3)*2^(n-4) (A001787).

LINKS

Alois P. Heinz, Rows n = 0..300, flattened

FORMULA

G.f.: G(t,z) = 1/[1-2z+(1-t)z^4]. T(n,k) = 2T(n-1,k)-T(n-4,k)+T(n-4,k-1) (n>=4,k>=1).

EXAMPLE

T(9,2) = 6 because we have aa0, aa1, a0a, a1a, 0aa and 1aa, where a=0011.

Triangle starts:

1;

2;

4;

8;

15, 1;

28, 4;

52, 12;

96, 32;

MAPLE

G:=1/(1-2*z+(1-t)*z^4): Gser:=simplify(series(G, z=0, 23)): P[0]:=1: for n from 1 to 19 do P[n]:=sort(coeff(Gser, z^n)) od: for n from 0 to 19 do seq(coeff(P[n], t, j), j=0..floor(n/4)) od; # yields sequence in triangular form

MATHEMATICA

nn=12; c=0; 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, A008937, A118885, A001787.

Sequence in context: A093483 A028398 A155249 * A118890 A118869 A118897

Adjacent sequences:  A118881 A118882 A118883 * A118885 A118886 A118887

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, May 03 2006

STATUS

approved

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Last modified January 26 11:27 EST 2021. Contains 340438 sequences. (Running on oeis4.)