A093335 a(0) = 0, a(1) = 1 and for n >= 0, a(n+2) = int(4 * a(n) * a(n+1) / (a(n) + a(n+1))).

1, 1, 2, 2, 4, 5, 8, 12, 19, 29, 45, 70, 109, 170, 265, 414, 646, 1009, 1575, 2460, 3840, 5997, 9364, 14622, 22833, 35654, 55676, 86940, 135762, 211998, 331047, 516946, 807239, 1260545, 1968408, 3073772, 4799858, 7495231, 11704199, 18276724

Offset

0,3

Comments

Harmonic-mean analog of Fibonacci sequence.

Terms in the Fibonacci sequence are equivalent to twice the arithmetic mean of the previous two terms. Terms in this sequence are floor(twice the harmonic mean of the previous two terms).

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Example

a(5) = 4 because a(5) = int(4 * (a(3) * a(4) / (a(3)+a(4))) = int(16/4) = 4.

Mathematica

nxt[{a_, b_}]:={b, Floor[2*HarmonicMean[{a, b}]]}; Join[{1}, Transpose[ NestList[ nxt, {1, 2}, 40]][[1]]] (* Harvey P. Dale, Mar 04 2015 *)

Crossrefs

Cf. A000045, A093333, A093332.

Sequence in context: A274154 A274153 A079501 * A093333 A116085 A329692

Adjacent sequences: A093332 A093333 A093334 * A093336 A093337 A093338

Keyword

easy,nonn

Author

Robert A. Stump (rstump_2004(AT)yahoo.com), Apr 25 2004

Status

approved