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A055168
Cumulative counting sequence: method B (noun,adjective)-pairs with first term 0.
11
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, 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, 2, 9, 3, 7, 4, 7, 5, 7, 6, 7, 9, 2, 7, 1, 11, 1, 8, 1, 0, 9, 1, 17
OFFSET
1,5
COMMENTS
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
LINKS
EXAMPLE
Start with 0, then 0,1; then 2,0 and 1,1; etc.
Writing pairs vertically, the initial segments are
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
...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
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
MATHEMATICA
s = {0}; Do[s = Flatten[{s, {#, Count[s, #]} & /@ DeleteDuplicates[s]}], {24}]; s (* Peter J. C. Moses, Mar 21 2013 *)
CROSSREFS
See A001155 and A022470 for well-known counting sequences using methods A and B.
Sequence in context: A340031 A029352 A340011 * A085144 A156578 A171846
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 27 2000
EXTENSIONS
Conjecture removed by Clark Kimberling, Oct 24 2009
STATUS
approved