A173278 Partial sums of A000048.

1, 2, 3, 4, 6, 9, 14, 23, 39, 67, 118, 211, 381, 696, 1281, 2372, 4420, 8275, 15555, 29352, 55566, 105495, 200820, 383181, 732701, 1403789, 2694344, 5179848, 9973338, 19229733, 37125412, 71762245, 138871109, 269021602, 521666737

Offset

0,2

Comments

Partial sums of number of n-bead necklaces with beads of 2 colors and primitive period n, when turning over is not allowed but the two colors can be interchanged. Partial sums of 2n-bead balanced binary necklaces of fundamental period 2n that are equivalent to their complements. Partial sums of binary Lyndon words of length n with an odd number of 1's. Partial sums of number of binary Lyndon words with trace 1 over GF(2). Partial sums of number of binary irreducible polynomials of degree n having trace 1. For more equivalences see A000048. The subsequence of primes in this partial sum begins: 2, 3, 23, 67, 211, 1403789.

Links

Table of n, a(n) for n=0..34.

Example

a(35) = 1 + 1 + 1 + 1 + 2 + 3 + 5 + 9 + 16 + 28 + 51 + 93 + 170 + 315 + 585 + 1091 + 2048 + 3855 + 7280 + 13797 + 26214 + 49929 + 95325 + 182361 + 349520 + 671088 + 1290555 + 2485504 + 4793490 + 9256395 + 17895679 + 34636833 + 67108864 + 130150493 + 252645135 + 490853403.

Crossrefs

Cf. A000048.

Sequence in context: A000381 A350588 A001115 * A173289 A096824 A192488

Adjacent sequences: A173275 A173276 A173277 * A173279 A173280 A173281

Keyword

nonn

Author

Jonathan Vos Post, Feb 14 2010

Status

approved