A303430 Number of binary words of length n with exactly twice as many occurrences of subword 101 as occurrences of subword 010.

1, 2, 4, 6, 10, 17, 28, 49, 84, 148, 263, 472, 858, 1568, 2893, 5372, 10034, 18824, 35428, 66898, 126683, 240483, 457334, 870956, 1660850, 3171112, 6061596, 11597587, 22206775, 42551339, 81591256, 156553245, 300565760, 577360360, 1109601934, 2133499936

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..3448

Example

a(0) = 1: the empty word.
a(1) = 2: 0, 1.
a(2) = 4: 00, 01, 10, 11.
a(3) = 6: 000, 001, 011, 100, 110, 111.
a(4) = 10: 0000, 0001, 0011, 0110, 0111, 1000, 1001, 1100, 1110, 1111.
a(5) = 17: 00000, 00001, 00011, 00110, 00111, 01100, 01110, 01111, 10000, 10001, 10011, 10101, 11000, 11001, 11100, 11110, 11111.

Maple

b:= proc(n, t, h, c) option remember; `if`(abs(c)>2*n, 0,
     `if`(n=0, 1, b(n-1, [1, 3, 1][t], 2, c-`if`(h=3, 2, 0))
                + b(n-1, 2, [1, 3, 1][h], c+`if`(t=3, 1, 0))))
    end:
a:= n-> b(n, 1$2, 0):
seq(a(n), n=0..50);

Crossrefs

Cf. A005251, A164146, A260668, A284449.

Column k=2 of A303696.

Sequence in context: A014216 A192683 A079961 * A144023 A018164 A321403

Adjacent sequences: A303427 A303428 A303429 * A303431 A303432 A303433

Keyword

nonn

Author

Alois P. Heinz, Apr 23 2018

Status

approved