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A217760 Cumulative counting sequence: (adjective-before-noun) pairs with first term 0; see Comments.

%I A217760 #10 Dec 04 2016 19:46:30
%S A217760 0,1,0,2,0,1,1,3,0,3,1,1,2,4,0,5,1,2,2,2,3,5,0,6,1,5,2,3,3,1,4,1,5,6,
%T A217760 0,9,1,6,2,5,3,2,4,4,5,1,6,7,0,11,1,8,2,6,3,4,4,6,5,4,6,1,9,8,0,13,1,9
%N A217760 Cumulative counting sequence: (adjective-before-noun) pairs with first term 0; see Comments.
%C A217760 Write 0 followed by segments defined inductively as follows: each segment
%C A217760 tells how many times each previously written integer occurs, in the order
%C A217760 of first occurrence.  This is Method A (adjective-before-noun pairs); for
%C A217760 Method B (noun-before-adjective), see A055168.  The sequence A217760 was
%C A217760 originally A055186 (Apr 27 2000); the present A055186 has a shorter
%C A217760 definition and differs from A217760 beginning at the 62nd term.
%H A217760 Clark Kimberling, <a href="/A217760/b217760.txt">Table of n, a(n) for n = 1..9666</a>
%H A217760 Clark Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/unsolved.html">Unsolved Problems and Rewards, Problem 4</a>
%e A217760 Start with 0, followed by the adjective-noun pair 1,0; followed by
%e A217760 adjective-noun pairs 2,0 then 1,1; etc. Writing the pairs vertically,
%e A217760 the initial segments are
%e A217760 0..1..2 1..3 3 1..4 5 2 2..5 6 5 3 1 1..6 9 6 5 2 4 1..7 11 8 6 4 6 4 1
%e A217760 ...0..0 1..0 1 2..0 1 2 3..0 1 2 3 4 5..0 1 2 3 4 5 6..0 1  2 3 4 5 6 9
%e A217760 The order of appearance is 0,1,2,3,4,5,6,9,7,11,8,... conjectured at A055170 to include all the nonnegative integers.
%t A217760 s = {0}; Do[s = Flatten[{s, {Count[s, #], #} & /@ DeleteDuplicates[s]}], {14}]; s  (* A217760 *)
%t A217760 s = {0}; Do[s = Flatten[{s, {Count[s, #], #} & /@ (a = DeleteDuplicates[s])}], {24}]; a;  (* A055170 *) (* _Peter J. C. Moses_, Mar 21 2013 *)
%Y A217760 Cf. A055170, A055186.
%K A217760 nonn,easy
%O A217760 1,4
%A A217760 _Clark Kimberling_, Mar 24 2013