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 A242257 Number of binary words of length n that contain all sixteen 4-bit words as (possibly overlapping) contiguous subwords. 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 19,1 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). LINKS Alois P. Heinz, Table of n, a(n) for n = 19..1000 Eric Weisstein's World of Mathematics, Coin Tossing Wikipedia, Deterministic finite automaton EXAMPLE a(19) = 256: 0000100110101111000, 0000100111101011000, 0000101001101111000, ..., 1111010110010000111, 1111011000010100111, 1111011001010000111. 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); CROSSREFS Cf. A001146, A052944, A242167, A242206, A242323, A243820. Sequence in context: A205090 A231943 A206327 * A206320 A237315 A237309 Adjacent sequences: A242254 A242255 A242256 * A242258 A242259 A242260 KEYWORD nonn AUTHOR Alois P. Heinz, May 09 2014 STATUS approved

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Last modified March 26 04:20 EDT 2023. Contains 361529 sequences. (Running on oeis4.)