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A164397 Number of binary strings of length n with no substrings equal to 0001 or 0111. 2
1, 2, 4, 8, 14, 24, 41, 68, 112, 184, 300, 488, 793, 1286, 2084, 3376, 5466, 8848, 14321, 23176, 37504, 60688, 98200, 158896, 257105, 416010, 673124, 1089144, 1762278, 2851432, 4613721, 7465164, 12078896, 19544072, 31622980, 51167064, 82790057, 133957134 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..2000 (first 500 terms from R. H. Hardin)

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

FORMULA

G.f.: -1/((x^2+x+1)*(x^2+x-1)*(x-1)^2). - R. J. Mathar, Nov 30 2011

MATHEMATICA

LinearRecurrence[{2, 0, 0, -2, 0, 1}, {14, 24, 41, 68, 112, 184}, 40] (* Harvey P. Dale, Jan 23 2012 *)

CoefficientList[Series[-1 (14 - 4 x - 7 x^2 - 14 x^3 + 4 x^4 + 8 x^5) / ((1 + x + x^2) (x^2 + x - 1) (x - 1)^2), {x, 0, 33}], x] (* Vincenzo Librandi, Sep 19 2017 *)

PROG

(PARI) x='x+O('x^50); Vec(-x^4*(14-4*x-7*x^2-14*x^3+4*x^4+8*x^5)/( (1+x+x^2)*(x^2+x-1)*(x-1)^2 )) \\ G. C. Greubel, Sep 18 2017

(MAGMA) I:=[14, 24, 41, 68, 112, 184]; [n le 6 select I[n] else 2*Self(n-1)-2*Self(n-4)+Self(n-6): n in [1..40]]; // Vincenzo Librandi, Sep 19 2017

CROSSREFS

Cf. A178982.

Sequence in context: A182747 A164406 A178982 * A164174 A164396 A164400

Adjacent sequences:  A164394 A164395 A164396 * A164398 A164399 A164400

KEYWORD

nonn,easy

AUTHOR

R. H. Hardin, Aug 14 2009

EXTENSIONS

Edited by Alois P. Heinz, Oct 27 2017

STATUS

approved

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Last modified December 7 13:08 EST 2021. Contains 349581 sequences. (Running on oeis4.)