|
%I #2 Mar 30 2012 18:40:51
%S 1,2,3,4,6,9,14,23,39,67,118,211,381,696,1281,2372,4420,8275,15555,
%T 29352,55566,105495,200820,383181,732701,1403789,2694344,5179848,
%U 9973338,19229733,37125412,71762245,138871109,269021602,521666737
%N Partial sums of A000048.
%C 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.
%e 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.
%Y Cf. A000048.
%K nonn
%O 0,2
%A _Jonathan Vos Post_, Feb 14 2010
|
