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

0,2

Links

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

Example

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.

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);

Crossrefs

Column k=3 of A303696.

Sequence in context: A128588 A023613 A306293 * A065795 A293077 A000801

Adjacent sequences: A307792 A307793 A307794 * A307796 A307797 A307798

Keyword

nonn

Author

Alois P. Heinz, Apr 29 2019

Status

approved