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%I #25 Nov 12 2022 10:49:40
%S 0,0,1,0,2,1,1,0,3,1,3,2,1,0,4,1,5,2,2,3,2,0,5,1,6,2,5,3,3,4,1,5,1,0,
%T 6,1,9,2,6,3,5,4,2,5,4,6,1,0,7,1,11,2,8,3,6,4,4,5,6,6,4,9,1,0,8,1,13,
%U 2,9,3,7,4,7,5,7,6,7,9,2,7,1,11,1,8,1,0,9,1,17
%N Cumulative counting sequence: method B (noun,adjective)-pairs with first term 0.
%C Write 0 followed by segments defined inductively as follows: each segment tells how many times each previously written integer occurs, stating first the integer being counted and then its frequency. This is Method B (noun-before-adjective); for Method A (adjective-before-noun), see A217760. - _Clark Kimberling_, Mar 25 2013
%H Seiichi Manyama, <a href="/A055168/b055168.txt">Table of n, a(n) for n = 1..10000</a>
%e Start with 0, then 0,1; then 2,0 and 1,1; etc.
%e Writing pairs vertically, the initial segments are
%e 0..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 ...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 3 1
%e The 5th segment tells that 0 has been written 4 times, 1 5 times, 2 2 times, and 3 2 times. The nouns are 1 2 3; the adjectives, 5 2 2. - _Clark Kimberling_, Mar 25 2013
%t s = {0}; Do[s = Flatten[{s, {#,Count[s, #]} & /@ DeleteDuplicates[s]}], {24}]; s (* _Peter J. C. Moses_, Mar 21 2013 *)
%Y Cf. A217760, A055170.
%Y Cf. A055171, A055174, A055177, A055180, A055183.
%Y See A001155 and A022470 for well-known counting sequences using methods A and B.
%K nonn
%O 1,5
%A _Clark Kimberling_, Apr 27 2000
%E Conjecture removed by _Clark Kimberling_, Oct 24 2009
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