A177736 Partial sums of A006156.

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

Author

Jonathan Vos Post, May 12 2010

Keywords

• nonn

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.

Crossrefs

Cf. A006156, A060688.

Formula

a(n) = Sum_{i=0..n} A006156(i).