login
A177736
Partial sums of A006156.
0
1, 4, 10, 22, 40, 70, 112, 172, 250, 358, 502, 706, 970, 1312, 1768, 2386, 3184, 4228, 5620, 7450, 9838, 13018, 17164, 22582, 29614, 38812, 50704, 66190, 86410, 112834, 147256, 192118, 250564, 326686, 425962, 555478, 724024, 943540, 1229290
OFFSET
0,2
COMMENTS
Partial sums of number of ternary squarefree words of length n. Is this always even after a(0) = 1? If so, there are no prime elements, and the subsequence of semiprime elements begins: 358, 502, 706, 2386, 9838, 112834, 192118, 425962. As Weisstein writes in the Mathworld link from A006156: A "square" word consists of two identical adjacent subwords (for example, acbacb). A squarefree word contains no square words as subwords (for example, abcacbabcb). The only squarefree binary words are a, b, ab, ba, aba, and bab (since aa, bb, aaa, aab, abb, baa, bba, and bbb contain square identical adjacent subwords a, b, a, a, b, a, b, and b, respectively). However, there are arbitrarily long ternary squarefree words.
FORMULA
a(n) = Sum_{i=0..n} A006156(i).
CROSSREFS
Sequence in context: A339609 A008248 A301243 * A061777 A298030 A155369
KEYWORD
nonn
AUTHOR
Jonathan Vos Post, May 12 2010
STATUS
approved