A213290 - OEIS

%I #12 Mar 14 2015 20:29:52

%S 1,2,4,5,9,14,27,46,91,162,323,589,1177,2179,4357,8152,16303,30746,

%T 61491,116689,233377,445095,890189,1704795,3409589,6552379,13104757,

%U 25258601,50517201,97617061,195234121,378098956,756197911,1467343306,2934686611,5704370761

%N Number of n-length words w over binary alphabet such that for every prefix z of w we have #(z,a_i) = 0 or #(z,a_i) >= #(z,a_j) for all j>i and #(z,a_i) counts the occurrences of the i-th letter in z.

%H Alois P. Heinz, <a href="/A213290/b213290.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A001405(n) + A001405(n-2) + A057427(n).

%F a(n) = A182172(n,2) + A182172(n-2,2) + A057427(n).

%e a(0) = 1: the empty word.

%e a(1) = 2: a, b for alphabet {a,b}.

%e a(2) = 4: aa, ab, ba, bb.

%e a(3) = 5: aaa, aab, aba, baa, bbb.

%e a(4) = 9: aaaa, aaab, aaba, aabb, abaa, abab, baaa, baab, bbbb.

%e a(5) = 14: aaaaa, aaaab, aaaba, aaabb, aabaa, aabab, aabba, abaaa, abaab, ababa, baaaa, baaab, baaba, bbbbb.

%p b:= n-> `if`(n<0, 0, binomial(n, ceil(n/2))):

%p a:= n-> b(n) +b(n-2) +`if`(n>0, 1, 0):

%p seq(a(n), n=0..40);

%Y Column k=2 of A213276.

%Y Cf. A001405, A057427, A182172.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Jun 08 2012