A242257 Number of binary words of length n that contain all sixteen 4-bit words as (possibly overlapping) contiguous subwords.

256, 1344, 5376, 19028, 61808, 188474, 547350, 1522758, 4083256, 10620590, 26912658, 66671138, 161950112, 386663750, 909204980, 2109158718, 4834062186, 10960141396, 24608994426, 54771900982, 120939714274, 265121486866, 577386711942, 1249925021562, 2691031388142

Offset: 19

Author

Alois P. Heinz, May 09 2014

Keywords

• nonn

Comments

The expected wait time to see all sixteen 4-bit words is Sum_{n>=0} (1-a(n)/2^n) ~ 58.632877... (with a(n) = 0 for 0 <= n <= 18).

Examples

			a(19) = 256: 0000100110101111000, 0000100111101011000, 0000101001101111000, ..., 1111010110010000111, 1111011000010100111, 1111011001010000111.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 19..2000
• Eric Weisstein's World of Mathematics, Coin Tossing
• Wikipedia, Deterministic finite automaton

Crossrefs

Cf. A001146, A052944, A242167, A242206, A242323, A243820.

Programs

Maple

b:=
proc(n, l) option remember; local m; m:= min(l[]);
  `if`(m=5, 2^n, `if`(5-m>n, 0,        b(n-1, [   [2, 3, 4, 5, 5][l[1]],
  [1, 1, 1, 1, 5][l[2]],  [2, 3, 4, 4, 5][l[3]],  [1, 1, 1, 5, 5][l[4]],
  [2, 3, 3, 5, 5][l[5]],  [1, 1, 4, 1, 5][l[6]],  [2, 2, 4, 5, 5][l[7]],
  [1, 3, 1, 3, 5][l[8]],  [1, 3, 4, 5, 5][l[9]],  [2, 2, 2, 2, 5][l[10]],
  [2, 3, 3, 2, 5][l[11]], [1, 1, 4, 5, 5][l[12]], [2, 2, 2, 5, 5][l[13]],
  [1, 3, 4, 1, 5][l[14]], [2, 2, 4, 2, 5][l[15]], [1, 3, 1, 5, 5][l[16]]])+
  b(n-1, [                [1, 1, 1, 1, 5][l[1]],  [2, 3, 4, 5, 5][l[2]],
  [1, 1, 1, 5, 5][l[3]],  [2, 3, 4, 4, 5][l[4]],  [1, 1, 4, 1, 5][l[5]],
  [2, 3, 3, 5, 5][l[6]],  [1, 3, 1, 3, 5][l[7]],  [2, 2, 4, 5, 5][l[8]],
  [2, 2, 2, 2, 5][l[9]],  [1, 3, 4, 5, 5][l[10]], [1, 1, 4, 5, 5][l[11]],
  [2, 3, 3, 2, 5][l[12]], [1, 3, 4, 1, 5][l[13]], [2, 2, 2, 5, 5][l[14]],
  [1, 3, 1, 5, 5][l[15]], [2, 2, 4, 2, 5][l[16]]])))
end:
a:= n-> b(n, [1$16]):
seq(a(n), n=19..40);