A035214 - OEIS

A035214

2 followed by a run of n 1's.

2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000

Mohammad K. Azarian, Remarks and Conjectures Regarding Combinatorics of Discrete Partial Functions, Int'l Math. Forum (2022) Vol. 17, No. 3, 129-141. See Conjecture 4.5, p. 137.

FORMULA

a(n) = 2 if n is a triangular number, otherwise 1.

Equals A010054(n) + 1.

a(n) = floor((3-cos(Pi*sqrt(8*n+1)))/2). - Carl R. White, Mar 18 2006

MATHEMATICA

Table[(SquaresR[1, 8*n + 1] + 2)/2, {n, 0, 100}] (* or *) Table[Floor[(3 - Cos[Pi*Sqrt[8*n + 1]])/2], {n, 0, 100}] (* G. C. Greubel, May 14 2017 *)