A307795 Number of binary words of length n with three times as many occurrences of subword 101 as occurrences of subword 010.

1, 2, 4, 6, 10, 16, 26, 42, 70, 116, 196, 332, 572, 996, 1758, 3134, 5650, 10276, 18836, 34720, 64310, 119582, 223066, 417028, 780876, 1463800, 2746304, 5155556, 9682418, 18189458, 34178904, 64236714, 120749592, 227018306, 426886298, 802872340, 1510325700

Offset: 0

Author

Alois P. Heinz, Apr 29 2019

Keywords

• nonn

Examples

			a(8) = 70: 00000000, 00000001, 00000011, 00000110, 00000111, 00001100, 00001110, 00001111, 00011000, 00011001, 00011100, 00011110, 00011111, 00110000, 00110001, 00110011, 00111000, 00111001, 00111100, 00111110, 00111111, 01100000, 01100001, 01100011, 01100110, 01100111, 01110000, 01110001, 01110011, 01111000, 01111001, 01111100, 01111110, 01111111, 10000000, 10000001, 10000011, 10000110, 10000111, 10001100, 10001110, 10001111, 10011000, 10011001, 10011100, 10011110, 10011111, 10101101, 10110101, 11000000, 11000001, 11000011, 11000110, 11000111, 11001100, 11001110, 11001111, 11100000, 11100001, 11100011, 11100110, 11100111, 11110000, 11110001, 11110011, 11111000, 11111001, 11111100, 11111110, 11111111.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..3573

Crossrefs

Column k=3 of A303696.

Programs

Maple

b:= proc(n, t, h, c) option remember; `if`(abs(c)>3*n, 0,
     `if`(n=0, 1, b(n-1, [1, 3, 1][t], 2, c-`if`(h=3, 3, 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);