A184364 - OEIS

%I #10 Dec 24 2012 20:43:14

%S 2,6,4,14,14,8,30,38,30,16,62,90,86,62,32,126,200,218,182,126,64,254,

%T 428,516,474,374,254,128,510,896,1170,1156,986,758,510,256,1022,1850,

%U 2576,2698,2436,2010,1526,1022,512,2046,3786,5554,6118,5770,4996,4058,3062,2046,1024

%N 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.

%H Donatien Bénéat, <a href="/A184364/b184364.txt">Rows n=1..20 of triangle, flattened</a>

%e For example, let n=3, k=2.

%e -------------------------------

%e word  number of different subwords of length 2

%e -------------------------------

%e 000   1

%e 001   2

%e 010   2

%e 011   2

%e 100   2

%e 101   2

%e 110   2

%e 111   1

%e ----------

%e total: 14 = a(3,2)

%t nbSubWords[m_, k_] := Length[DeleteDuplicates[Partition[m, k, 1]]];

%t a[n_, k_] := Plus @@ (nbSubWords[#, k] & /@ Tuples[{0, 1}, n])

%K nonn,tabl

%O 1,1

%A _Donatien Bénéat_, Dec 24 2012