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

0,2

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.

Links

Table of n, a(n) for n=0..38.

Formula

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

Crossrefs

Cf. A006156, A060688.

Sequence in context: A339609 A008248 A301243 * A061777 A298030 A155369

Adjacent sequences: A177733 A177734 A177735 * A177737 A177738 A177739

Keyword

nonn

Author

Jonathan Vos Post, May 12 2010

Status

approved