|
| |
|
|
A336861
|
|
a(n) = ceiling((n-1-sqrt(n+1))/2).
|
|
1
|
|
|
|
0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,6
|
|
|
COMMENTS
|
a(n) is a lower bound for the number of items outside the instance of n-1 at one end of a Colombian variant Langford pairing (A336747). For example, one of the most lop-sided pairings for n=7 is 4 1 6 1 7 4 3 5 2 6 3 2 7 5, and there are a(n)=2 items to the left of the first '6'. This bound is tight until at least n=184.
|
|
|
LINKS
|
|
|
|
MATHEMATICA
|
Table[Ceiling[(n - 1 - Sqrt[n + 1])/2], {n, 1, 100}] (* Amiram Eldar, Aug 21 2020 *)
|
|
|
PROG
|
(Magma) [Ceiling((n-1-Sqrt(n+1))/2) : n in [1..100]]; // Wesley Ivan Hurt, Aug 21 2020
(PARI) a(n) = ceil((n-1-sqrt(n+1))/2); \\ Michel Marcus, Aug 19 2020
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
