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A164485 Number of binary strings of length n with no substrings equal to 0001, 1000 or 1001. 1
13, 21, 33, 53, 85, 137, 221, 357, 577, 933, 1509, 2441, 3949, 6389, 10337, 16725, 27061, 43785, 70845, 114629, 185473, 300101, 485573, 785673, 1271245, 2056917, 3328161, 5385077, 8713237, 14098313, 22811549, 36909861, 59721409, 96631269 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,1

LINKS

R. H. Hardin, Table of n, a(n) for n = 4..500

Martin Griffiths, On a Matrix Arising from a Family of Iterated Self-Compositions, Journal of Integer Sequences, 18 (2015), #15.11.8.

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

FORMULA

G.f. -x^4*(-13 + 5*x + 9*x^2) / ((x - 1)*(x^2 + x - 1)). - R. J. Mathar, Jan 19 2011

a(n) = 4*Fibonacci(n) + 1. - Bruno Berselli, Jul 26 2017

From Colin Barker, Jul 26 2017: (Start)

a(n) = 1 - (4*(((1 - sqrt(5))/2)^n - ((1 + sqrt(5))/2)^n))/sqrt(5) for n>3.

a(n) = 2*a(n-1) - a(n-3) for n>6.

(End)

PROG

(PARI) Vec(-x^4*(-13 + 5*x + 9*x^2) / ((x - 1)*(x^2 + x - 1)) + O(x^60)) \\ Colin Barker, Jul 26 2017

(Python)

from sympy import fibonacci

def a(n): return 4*fibonacci(n) + 1

print([a(n) for n in range(4, 101)]) # Indranil Ghosh, Jul 26 2017

CROSSREFS

Sequence in context: A164488 A164436 A164498 * A164447 A057200 A164454

Adjacent sequences:  A164482 A164483 A164484 * A164486 A164487 A164488

KEYWORD

nonn,easy

AUTHOR

R. H. Hardin Aug 14 2009

STATUS

approved

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Last modified October 26 04:27 EDT 2021. Contains 348256 sequences. (Running on oeis4.)