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A260697 Number of binary words w of length n with equal numbers of 010 and 101 subwords such that for every prefix of w the number of occurrences of subword 101 is larger than or equal to the number of occurrences of subword 010. 5
1, 2, 4, 6, 11, 18, 32, 54, 95, 164, 291, 514, 923, 1656, 3000, 5442, 9942, 18216, 33564, 62040, 115167, 214404, 400497, 750070, 1408734, 2652088, 5004833, 9464616, 17935137, 34049044, 64754844, 123351410, 235335966, 449632300, 860241606, 1647932000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

EXAMPLE

a(3) = 6: 000, 001, 011, 100, 110, 111.

a(4) = 11: 0000, 0001, 0011, 0110, 0111, 1000, 1001, 1010, 1100, 1110, 1111.

a(5) = 18: 00000, 00001, 00011, 00110, 00111, 01100, 01110, 01111, 10000, 10001, 10011, 10100, 11000, 11001, 11010, 11100, 11110, 11111.

a(10) = 291: 0000000000, 0000000001, 0000000011, ..., 0110101010, 1010101000, 1010101001, 1010101010, 1101010100, 1110101010, ..., 1111111100, 1111111110, 1111111111.

MAPLE

b:= proc(n, t, c) option remember;

     `if`(c<0, 0, `if`(n=0, `if`(c=0, 1, 0),

      b(n-1, [2, 4, 6, 4, 6, 4, 6][t], c-`if`(t=5, 1, 0))+

      b(n-1, [3, 5, 7, 5, 7, 5, 7][t], c+`if`(t=6, 1, 0))))

    end:

a:= n-> b(n, 1, 0):

seq(a(n), n=0..40);

# second Maple program:

a:= proc(n) option remember;

     `if`(n<7, [1, 2, 4, 6, 11, 18, 32][n+1],

     ((n+3)*(307*n^2-2357*n+196)              *a(n-1)

      -(19280-3372*n-5181*n^2+719*n^3)        *a(n-2)

      +(2*(6582+268*n^3-2857*n^2+6959*n))     *a(n-3)

      +(2*(-3307*n^2+1151*n+384*n^3+9052))    *a(n-4)

      -(2*(1016*n^3-12133*n^2+38927*n-28304)) *a(n-5)

      +(4*(27387*n+431*n^3-38420-6108*n^2))   *a(n-6)

      -(4*(n-7))*(67*n-236)*(2*n-11)          *a(n-7)

      )/((2*(n+4))*(24*n^2-148*n-279)))

    end:

seq(a(n), n=0..40);

CROSSREFS

Cf. A118430, A164146, A255386, A260505, A260668.

Sequence in context: A185192 A007053 A005684 * A018167 A295831 A140443

Adjacent sequences:  A260694 A260695 A260696 * A260698 A260699 A260700

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 16 2015

STATUS

approved

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Last modified May 22 06:32 EDT 2019. Contains 323478 sequences. (Running on oeis4.)