A184219 a(n) = A184218(n)/A130703(n) unless A130703(n) = 0 in which case a(n) = 0.

0, 0, 0, 0, 1, 1, 2, 1, 1, 2, 3, 1, 1, 5, 4, 1, 5, 4, 5, 7, 1, 5, 9, 5, 1, 9, 10, 1, 9, 7, 8, 11, 1, 14, 11, 1, 7, 13, 10, 1, 13, 10, 11, 15, 1, 11, 20, 7, 5, 18, 14, 5, 17, 22, 14, 19, 11, 14, 19, 1, 1, 27, 16, 13, 27, 16, 26, 23

Offset

1,7

Comments

a(n) is the "level" of triangular numbers.

The decomposition of triangular numbers into weight * level + gap is A000217(n) = A130703(n) * a(n) + (n + 1) if a(n) > 0.

A184218(n) = A000217(n) - (n + 1) if A000217(n) - (n + 1) > (n + 1), 0 otherwise.

Links

Rémi Eismann, Table of n, a(n) for n = 1..10000

Example

For n = 3 we have A130703(3) = 0, hence a(3) = 0.
For n = 5 we have A184218(5)/A130703(5) = 9 / 9 = 1, hence a(5) = 1.
For n = 24 we have A184218(24)/A130703(24) = 275 / 55 = 5, hence a(24) = 5.

Crossrefs

Cf. A000217, A000027, A130703, A184218, A118534, A117078, A117563, A001223.

Sequence in context: A215204 A260876 A152650 * A180262 A161789 A109671

Adjacent sequences: A184216 A184217 A184218 * A184220 A184221 A184222

Keyword

nonn

Author

Rémi Eismann, Jan 10 2011

Status

approved