OFFSET

1,1

FORMULA

a(n) = 2*floor(sqrt(n)+1/2)+1. - Mikael Aaltonen, Jan 14 2015

From Robert Israel, Jan 14 2015: (Start)

G.f.: (x/(1-x))*(1+2*Sum_{m>=0} x^(m*(m+1))) = (x/(1-x))*(1+x^(-1/4)*theta_2(0,x)) where theta_2 is the second Jacobi theta function.

a(2n) = a(2n-1) = 2*A002024(n)+1.

a(n) = A001670(n)+1.

(End)

MAPLE

seq(2*n+1 $ 2*n, n=1..10); # Robert Israel, Jan 14 2015

PROG

(Python)

from math import isqrt

def A130829(n): return 1|((m:=isqrt(n))+int((n-m*(m+1)<<2)>=1)<<1) # Chai Wah Wu, Oct 17 2022

CROSSREFS

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jul 17 2007

STATUS

approved