This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A051068 #21 Feb 16 2019 12:12:20 %S A051068 0,1,2,2,3,4,4,5,6,7,8,9,9,10,11,11,12,13,14,15,16,16,17,18,18,19,20, %T A051068 20,21,22,22,23,24,24,25,26,27,28,29,29,30,31,31,32,33,34,35,36,36,37, %U A051068 38,38,39,40,40,41,42,42,43,44,44,45,46,47,48,49,49 %N A051068 Partial sums of A014578. %C A051068 Duplicate of A050294? [_Joerg Arndt_, Apr 27 2013] %C A051068 From _Michel Dekking_, Feb 10 2019: (Start) %C A051068 The answer to Joerg Arndt's question is: yes (modulo an offset). To see this, it suffices to prove that the two sequences of first differences Da and Db of a= A051068 and b:=A050294 are equal. Clearly the sequence Da of first differences of a is the sequence A014578. According to Philippe Deleham (2004), Da equals 0x = 0110110111110..., where x is the fixed point of the morphism 0->111, 1->110. %C A051068 From _Vladimir Shevelev_ (2011) we know a formula for b=A050294: b(n) = n-b(floor(n/3)). This gives that the sequence of first differences Db:=(b(n+1)-b(n)) of b satisfies %C A051068 Db(3m+1) = Db(3m+2) = 1, and Db(3m+3) = 1 - Db(m). %C A051068 This implies that Db = x, the fixed point of 0->111, 1->110. %C A051068 (End) %F A051068 a(3^n) = A015518(n+1) = -(-1)^n*A014983(n+1). - _Philippe Deléham_, Mar 31 2004 %Y A051068 Cf. A014578, A051069, A050294. %K A051068 nonn %O A051068 0,3 %A A051068 _N. J. A. Sloane_, _Gary W. Adamson_