A336861 a(n) = ceiling((n-1-sqrt(n+1))/2).

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

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

Table of n, a(n) for n=1..72.

Edward Moody, Java program for enumerating Colombian Langford pairings

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

Cf. A336747.

Sequence in context: A183142 A121830 A020911 * A029125 A074990 A102605

Adjacent sequences: A336858 A336859 A336860 * A336862 A336863 A336864

Keyword

nonn,easy

Author

Edward Moody, Aug 16 2020

Status

approved