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A260668 Number of binary words of length n such that for every prefix the number of occurrences of subword 101 is larger than or equal to the number of occurrences of subword 010. 5
1, 2, 4, 7, 13, 24, 45, 84, 158, 298, 566, 1079, 2066, 3966, 7635, 14730, 28484, 55188, 107130, 208294, 405594, 790812, 1543766, 3016923, 5901858, 11556244, 22647431, 44418613, 87182680, 171234318, 336532357, 661788956, 1302124526, 2563365624, 5048704640 (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(5) = 2^5 - 8 = 24: 00000, 00001, 00011, 00110, 00111, 01100, 01101, 01110, 01111, 10000, 10001, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111. These 8 words are not counted: 00010, 00100, 00101, 01000, 01001, 01010, 01011, 10010.

MAPLE

b:= proc(n, t, c) option remember; `if`(c<0, 0, `if`(n=0, 1,

      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<6, [1, 2, 4, 7, 13, 24][n+1],

      ((680+1441*n-444*n^2+35*n^3)        *a(n-1)

       -(4*(-112+625*n-179*n^2+14*n^3))   *a(n-2)

       +(2*(1521-656*n+63*n^2))           *a(n-3)

       +(2*(-9442+5295*n-947*n^2+56*n^3)) *a(n-4)

       -(4*(-6721+3413*n-591*n^2+35*n^3)) *a(n-5)

       +(4*(2*n-11))*(7*n^2-79*n+254)     *a(n-6)

        )/((n+1)*(7*n^2-93*n+340)))

    end:

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

CROSSREFS

Cf. A118430, A164146, A255386, A260505, A260697, A303430.

Sequence in context: A059633 A088353 A192654 * A018184 A192675 A018185

Adjacent sequences:  A260665 A260666 A260667 * A260669 A260670 A260671

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Nov 14 2015

STATUS

approved

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Last modified May 27 22:39 EDT 2022. Contains 354110 sequences. (Running on oeis4.)