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A238361 Number of length n binary words that contain 111 but do not contain 000 (as contiguous subwords). 1
0, 0, 0, 1, 3, 8, 18, 39, 81, 164, 326, 639, 1239, 2382, 4548, 8635, 16319, 30722, 57650, 107885, 201425, 375322, 698162, 1296801, 2405707, 4457984, 8253228, 15266969, 28220967, 52134000, 96257558, 177640983, 327696621, 604287700, 1113981922, 2053015399 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

For n>=1, a(n) = A000073(n+3) - 2*A000045(n+1).

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

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

FORMULA

G.f.: (x^3*(1 + x + x^2))/((1 - x - x^2)*(1 - x - x^2 - x^3)).

a(n) = 2*a(n-1) + a(n-2) - a(n-3) - 2*a(n-4) - a(n-5) for n>5. - Colin Barker, Nov 22 2019

EXAMPLE

There are a(6) = 18 such binary words:

01: 001110

02: 001111

03: 010111

04: 011100

05: 011101

06: 011110

07: 011111

08: 100111

09: 101110

10: 101111

11: 110111

12: 111001

13: 111010

14: 111011

15: 111100

16: 111101

17: 111110

18: 111111

MATHEMATICA

nn=30; CoefficientList[Series[(x^3+x^4+x^5)/(1-2x-x^2+x^3+2x^4+x^5), {x, 0, nn}], x]

PROG

(PARI) concat([0, 0, 0], Vec(x^3*(1 + x + x^2) / ((1 - x - x^2)*(1 - x - x^2 - x^3)) + O(x^40))) \\ Colin Barker, Nov 22 2019

CROSSREFS

Sequence in context: A117727 A117713 A128552 * A011377 A178420 A036385

Adjacent sequences: A238358 A238359 A238360 * A238362 A238363 A238364

KEYWORD

nonn,easy

AUTHOR

Geoffrey Critzer, Mar 08 2014

STATUS

approved

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Last modified December 4 02:16 EST 2022. Contains 358544 sequences. (Running on oeis4.)