

A129229


a(n)=Floor(n*r)a(n1), where r is the golden mean, (1+sqrt(5))/2.


3



0, 1, 2, 2, 4, 4, 5, 6, 6, 8, 8, 9, 10, 11, 11, 13, 12, 15, 14, 16, 16, 17, 18, 19, 19, 21, 21, 22, 23, 23, 25, 25, 26, 27, 28, 28, 30, 29, 32, 31, 33, 33, 34, 35, 36, 36, 38, 38, 39, 40, 40, 42, 42, 43, 44, 44, 46, 46, 47, 48, 49, 49, 51, 50, 53, 52, 54, 54, 56, 55, 58, 56, 60, 58
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OFFSET

0,3


LINKS

Table of n, a(n) for n=0..73.


FORMULA

a(n) = Floor(n*r)Floor((n1)*r)+Floor((n2)*r)...+d*Floor(r), where d=(1)^(n+1) and r = (1+sqrt(5))/2.


MATHEMATICA

nxt[{n_, a_}]:={n+1, Floor[GoldenRatio(n+1)]a}; Transpose[NestList[nxt, {0, 0}, 80]][[2]] (* Harvey P. Dale, Dec 08 2015 *)


CROSSREFS

Cf. A129230, A129231, A087851.
Sequence in context: A159267 A127311 A302929 * A219029 A090168 A337765
Adjacent sequences: A129226 A129227 A129228 * A129230 A129231 A129232


KEYWORD

nonn


AUTHOR

Clark Kimberling, Apr 04 2007, corrected Apr 04 2007


STATUS

approved



