

A055168


Cumulative counting sequence: method B (noun,adjective)pairs with first term 0.


10



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
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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 (nounbeforeadjective); for Method A (adjectivebeforenoun), see A217760.  Clark Kimberling Mar 25 2013


LINKS

Table of n, a(n) for n=1..89.


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

Cf. A217760, A055170, A055171.
See A001155 and A022470 for wellknown counting sequences using methods A and B.
Sequence in context: A116405 A281048 A029352 * A085144 A156578 A171846
Adjacent sequences: A055165 A055166 A055167 * A055169 A055170 A055171


KEYWORD

nonn


AUTHOR

Clark Kimberling, Apr 27 2000


EXTENSIONS

Conjecture removed.  Clark Kimberling, Oct 24 2009


STATUS

approved



