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

1,2

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]

Formula

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

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

Mathematica

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

Prog

(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

Crossrefs

Partial sums of A085002. A left inverse of A283766.

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

Sequence in context: A301426 A194222 A025779 * A119026 A064775 A260731

Adjacent sequences: A085000 A085001 A085002 * A085004 A085005 A085006

Keyword

nonn

Author

Benoit Cloitre, Jun 17 2003

Status

approved