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

Author

Alois P. Heinz, Apr 23 2018

Keywords

• nonn

Examples

			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.
		

Links

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

Crossrefs

Cf. A005251, A164146, A260668, A284449.

Column k=2 of A303696.

Programs

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);