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!)
A234590 Number of binary words of length n which have no 0^b 1 1 0^a 1 0 1 0^b - matches, where a=0, b=2. 2
1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1020, 2036, 4064, 8112, 16192, 32320, 64513, 128773, 257041, 513074, 1024136, 2044256, 4080496, 8144991, 16258042, 32452329, 64777398, 129300775, 258094504, 515176904, 1028333569, 2052634583, 4097219870, 8178372713 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

B. K. Miceli, J, Remmel, Minimal Overlapping Embeddings and Exact Matches in Words, PU. M. A., Vol. 23 (2012), No. 3, pp. 291-315.

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

FORMULA

G.f.: (1+x^7+x^8)/(1-2*x+x^7-x^8-x^9). - Alois P. Heinz, Jan 08 2014

MAPLE

a:= n-> coeff(series(-(x^8+x^7+1)/(x^9+x^8-x^7+2*x-1), x, n+1), x, n):

seq(a(n), n=0..60);  # Alois P. Heinz, Jan 08 2014

MATHEMATICA

a[n_ /; n<=8]:= 2^n; a[n_]:= a[n] =2*a[n-1] -a[n-7] +a[n-8] +a[n-9]; Table[a[n], {n, 0, 33}] (* Jean-Fran├žois Alcover, Mar 18 2014 *)

PROG

(PARI) my(x='x+O('x^60)); Vec((1+x^7+x^8)/(1-2*x+x^7-x^8-x^9)) \\ G. C. Greubel, Sep 14 2019

(MAGMA) I:=[1, 2, 4, 8, 16, 32, 64, 128, 256]; [n le 9 select I[n] else 2*Self(n-1) - Self(n-7) + Self(n-8) + Self(n-9): n in [1..60]]; // G. C. Greubel, Sep 14 2019

(Sage)

def A234590_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P((1+x^7+x^8)/(1-2*x+x^7-x^8-x^9)).list()

A234590_list(60) # G. C. Greubel, Sep 14 2019

(GAP) a:=[1, 2, 4, 8, 16, 32, 64, 128, 256];; for n in [10..60] do a[n]:=2*a[n-1] -a[n-7]+a[n-8]+a[n-9]; od; a; # G. C. Greubel, Sep 14 2019

CROSSREFS

Sequence in context: A008861 A145115 A172318 * A104144 A258800 A194632

Adjacent sequences:  A234587 A234588 A234589 * A234591 A234592 A234593

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jan 01 2014

EXTENSIONS

a(17)-a(33) from Alois P. Heinz, Jan 08 2014

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 February 28 23:19 EST 2020. Contains 332353 sequences. (Running on oeis4.)