login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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: A155249 A113553 A118884 * A118869 A118897 A098056

Adjacent sequences:  A118887 A118888 A118889 * A118891 A118892 A118893

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, May 04 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified November 20 13:59 EST 2017. Contains 294972 sequences.