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

Author

Jonathan Vos Post, Feb 14 2010

Keywords

• nonn

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.

Examples

			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.