A055168 Cumulative counting sequence: method B (noun,adjective)-pairs with first term 0.

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

Author

Clark Kimberling, Apr 27 2000

Keywords

• nonn

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

Examples

			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
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A217760, A055170.

Cf. A055171, A055174, A055177, A055180, A055183.

See A001155 and A022470 for well-known counting sequences using methods A and B.

Programs

Mathematica

s = {0}; Do[s = Flatten[{s, {#,Count[s, #]} & /@ DeleteDuplicates[s]}], {24}]; s (* Peter J. C. Moses, Mar 21 2013 *)

Extensions

Conjecture removed by Clark Kimberling, Oct 24 2009