|
| |
|
|
A012257
|
|
Table: row 1 is {1,1}; if row n is {r_1, ..., r_k} then row n+1 is {r_k 1's, r_{k-1} 2's, r_{k-2} 3's, etc.}.
|
|
8
| |
|
|
1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 2, 3, 4, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 7, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12, 13, 14
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,4
|
|
|
COMMENTS
| The shape of each row tends to a limit curve when scaled to a fixed size. It is the same limit curve as this continuous version: start with f_0=x over [0,1]; then repeatedly reverse (1-x), integrate from zero (x-x^2/2), scale to 1 (2x-x^2) and invert (1-sqrt(1-x)). For the limit curve we have f'(0) = F(1) = lim A011784(n+2)/(A011784(n+1)*A011784(n)) ~ 0.27887706 (obtained numerically) - Martin Fuller (martin_n_fuller(AT)btinternet.com), Aug 07 2006
|
|
|
FORMULA
| n-th row sum = A011784(n+2); e.g. 5-th row is {1, 1, 1, 2, 2, 3, 4} and the sum of elements is 1+1+1+2+2+3+4=14=A011784(7) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 06 2003
|
|
|
EXAMPLE
| {1,1}, {1,2}, {1,1,2}, {1,1,2,3}, {1,1,1,2,2,3,4}, {1,1,1,1,2,2,2,3,3,4,4,5,6,7}
|
|
|
CROSSREFS
| Cf. A011784.
Sequence in context: A161043 A029316 A104368 * A162320 A136610 A101022
Adjacent sequences: A012254 A012255 A012256 * A012258 A012259 A012260
|
|
|
KEYWORD
| nonn,tabf,nice
|
|
|
AUTHOR
| Lionel Levine (levine(AT)ultranet.com)
|
| |
|
|
