A085003 Partial sums of A085002.

1, 2, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 7, 7, 7, 8, 9, 10, 10, 10, 11, 12, 13, 13, 13, 13, 14, 15, 15, 15, 15, 16, 17, 18, 18, 18, 19, 20, 21, 21, 21, 22, 23, 24, 24, 24, 24, 25, 26, 26, 26, 26, 27, 28, 28, 28, 28, 29, 30, 31, 31, 31, 32, 33, 34, 34, 34, 34, 35, 36, 36, 36, 36, 37, 38

Offset: 1

Author

Benoit Cloitre, Jun 17 2003

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10946
• B. Cloitre, Graph of A085005(n) for n=1 up to 3874 [archive.org link]

Crossrefs

Partial sums of A085002. A left inverse of A283766.

Cf. A083035, A083036, A083037, A083038, A085004, A085005.

Programs

Mathematica

Accumulate[Table[Floor[GoldenRatio*n]-2*Floor[GoldenRatio*n/2],{n,110}]] (* Harvey P. Dale, Dec 11 2012 *)

PARI

sum(k=1,n,(k+sqrtint(5*k^2))%4>1) \\ Charles R Greathouse IV, Feb 07 2013
(Scheme, with memoization-macro definec)
(definec (A085003 n) (if (= 1 n) n (+ (A085002 n) (A085003 (- n 1)))))
;; Antti Karttunen, Mar 17 2017

Formula

a(n)=sum(k=1, n, A085002(k)).

a(A283766(n)) = n for all n >= 1. - Antti Karttunen, Mar 17 2017