login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A294049 Number of binary strings of length n avoiding substrings 1000, 1011, 1101, or 1111. 1
1, 2, 4, 8, 12, 18, 27, 41, 61, 88, 129, 189, 276, 401, 582, 848, 1233, 1791, 2601, 3779, 5492, 7976, 11584, 16826, 24441, 35500, 51558, 74885, 108767, 157976, 229445, 333247, 484017, 702994, 1021035, 1482962, 2153874, 3128318, 4543603, 6599180, 9584730 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,0,-2,0,1)

FORMULA

G.f.: (x+1)*(x^5+x^4-x^3-x^2-1)/((x-1)*(x^7+x^6-x^5-x^4-x^3-x^2+1)).

MAPLE

a:= n-> (Matrix(8, (i, j)-> `if`(i+1=j, 1, `if`(i=8,

    [1, 0, -2, 0$3, 1$2][j], 0)))^n. <<1, 2, 4, 8, 12, 18, 27, 41>>)[1$2]:

seq(a(n), n=0..45);

CROSSREFS

Cf. A164417, A164420.

Sequence in context: A224814 A224810 A074633 * A006500 A134181 A171645

Adjacent sequences:  A294046 A294047 A294048 * A294050 A294051 A294052

KEYWORD

nonn,easy

AUTHOR

Alois P. Heinz, Oct 22 2017

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
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 8 03:38 EDT 2020. Contains 335504 sequences. (Running on oeis4.)