A001670 - OEIS (original) (raw)

2, 2, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16

FORMULA

With a different offset: g.f. = Sum_{j>=0} 2*x^(j^2+i)/(1-x). - Ralf Stephan, Mar 11 2003

a(n) = a(n - a(n-2)) + 2; a(1)=2, a(2)=2.

a(n) = 2*round(sqrt(n)). (End)

G.f.: x^(3/4)*theta_2(0,x)/(1-x) where theta_2 is the second Jacobi theta function. - Robert Israel, Jan 14 2015

a(n) = 2*floor((sqrt(4*n-3)+1)/2). - Néstor Jofré, Apr 24 2017

MATHEMATICA

a[1]=2, a[2]=2, a[n_]:=a[n]=a[n-a[n-2]]+2 (* Branko Curgus, May 11 2010 *)

Flatten[Table[Table[n, {n}], {n, 2, 16, 2}]] (* Harvey P. Dale, May 31 2012 *)

PROG

(Magma) [2*Round(Sqrt(n)): n in [1..70]]; // Vincenzo Librandi, Jun 23 2011

(MATLAB) a = @(n) 2*floor((sqrt(4*n-3)+1)/2); % Néstor Jofré, Apr 24 2017

(Python)

from math import isqrt

def A001670(n): return (m:=isqrt(n))+int((n-m*(m+1)<<2)>=1)<<1 # Chai Wah Wu, Jul 29 2022