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A189663 Partial sums of A189661. 10
0, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 26, 27, 27, 28, 28, 28, 29, 29, 30, 30, 30, 31 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

See A189661.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

FORMULA

a(n) = 2*(n-1)-floor((n-1)*r), where r = (1+sqrt(5))/2 (the golden ratio). - corrected by R. J. Mathar, Sep 11 2011

a(n) = a(1+a(n-2))+a(n-1-a(n-2)), n>2. - Frank Ruskey, Dec 10 2011

a(1) = 0, a(2) = 1; a(n) = n - a(n-1) - a(n-a(n-1)) for n > 2. - Altug Alkan, Jun 24 2017

a(n) = ceiling((n-1)/r^2), where r = (1+sqrt(5))/2. -Jeffrey Shallit, Jul 02 2018

MATHEMATICA

(See A189661.)

Table[2 (n - 1) - Floor[(n - 1) (1 + Sqrt[5]) / 2], {n, 100}] (* Vincenzo Librandi, Jun 26 2017 *)

PROG

(Python)

l=[0, 0, 1]

for n in range(3, 101): l+=[n - l[n - 1] - l[n - l[n - 1]], ]

print l[1:] # Indranil Ghosh, Jun 24 2017, after Altug Alkan

(MAGMA) [2*(n-1)-Floor((n-1)*(1+Sqrt(5))/2): n in [1..100]]; // Vincenzo Librandi, Jun 26 2017

CROSSREFS

Cf. A001622, A189661, A189662, A026356.

Sequence in context: A057367 A032634 A057366 * A061375 A029920 A100719

Adjacent sequences:  A189660 A189661 A189662 * A189664 A189665 A189666

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 25 2011

STATUS

approved

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Last modified January 29 04:57 EST 2020. Contains 331335 sequences. (Running on oeis4.)