A184364 a(n,k) = 2^n times the average number of different subwords of length k in a random binary word of length n (prob 0 = prob 1 = 1/2), n>=1, 1<=k<=n; triangle read by rows.

2, 6, 4, 14, 14, 8, 30, 38, 30, 16, 62, 90, 86, 62, 32, 126, 200, 218, 182, 126, 64, 254, 428, 516, 474, 374, 254, 128, 510, 896, 1170, 1156, 986, 758, 510, 256, 1022, 1850, 2576, 2698, 2436, 2010, 1526, 1022, 512, 2046, 3786, 5554, 6118, 5770, 4996, 4058, 3062, 2046, 1024

Offset

1,1

Links

Donatien Bénéat, Rows n=1..20 of triangle, flattened

Example

For example, let n=3, k=2.
-------------------------------
word  number of different subwords of length 2
-------------------------------
000   1
001   2
010   2
011   2
100   2
101   2
110   2
111   1
----------
total: 14 = a(3,2)

Mathematica

nbSubWords[m_, k_] := Length[DeleteDuplicates[Partition[m, k, 1]]];
a[n_, k_] := Plus @@ (nbSubWords[#, k] & /@ Tuples[{0, 1}, n])

Crossrefs

Sequence in context: A268716 A204985 A255066 * A226569 A111807 A069914

Adjacent sequences: A184361 A184362 A184363 * A184365 A184366 A184367

Keyword

nonn,tabl

Author

Donatien Bénéat, Dec 24 2012

Status

approved