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A217760
Cumulative counting sequence: (adjective-before-noun) pairs with first term 0; see Comments.
10
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, 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
OFFSET
1,4
COMMENTS
Write 0 followed by segments defined inductively as follows: each segment
tells how many times each previously written integer occurs, in the order
of first occurrence. This is Method A (adjective-before-noun pairs); for
Method B (noun-before-adjective), see A055168. The sequence A217760 was
originally A055186 (Apr 27 2000); the present A055186 has a shorter
definition and differs from A217760 beginning at the 62nd term.
EXAMPLE
Start with 0, followed by the adjective-noun pair 1,0; followed by
adjective-noun pairs 2,0 then 1,1; etc. Writing the pairs vertically,
the initial segments are
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
...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
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.
MATHEMATICA
s = {0}; Do[s = Flatten[{s, {Count[s, #], #} & /@ DeleteDuplicates[s]}], {14}]; s (* A217760 *)
s = {0}; Do[s = Flatten[{s, {Count[s, #], #} & /@ (a = DeleteDuplicates[s])}], {24}]; a; (* A055170 *) (* Peter J. C. Moses, Mar 21 2013 *)
CROSSREFS
Sequence in context: A303337 A340502 A055186 * A339218 A263412 A321258
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 24 2013
STATUS
approved