A072930 - OEIS

A072930

a(1)=1, a(2)=10, a(n) = floor(a(n-1)/phi) + floor(a(n-2)/phi) where phi is the golden ratio (1+sqrt(5))/2 (if a(2) < 10 a(k) converges to an integer value).

1, 10, 6, 9, 8, 9, 9, 10, 11, 12, 13, 15, 17, 19, 21, 23, 26, 30, 34, 39, 45, 51, 58, 66, 75, 86, 99, 114, 131, 150, 172, 198, 228, 262, 301, 347, 400, 461, 531, 612, 706, 814, 939, 1083, 1249, 1440, 1660, 1914, 2207, 2546, 2937, 3388, 3908, 4508, 5201, 6000, 6922

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OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

Limit_{n -> infinity} a(n)/a(n-1) = (phi-1)/C = 1.1537213755417679... where C is the positive root of x^4 -x^3+2x-1 (C = 0.5356873867918...).

MATHEMATICA

RecurrenceTable[{a[1]==1, a[2]==10, a[n]==Floor[a[n-1]/GoldenRatio]+ Floor[a[n-2]/GoldenRatio]}, a, {n, 60}] (* Harvey P. Dale, Jan 27 2012 *)

CROSSREFS

Cf. A001622.

Sequence in context: A076366 A304879 A105155 * A071358 A167873 A369702

Adjacent sequences: A072927 A072928 A072929 * A072931 A072932 A072933

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Aug 13 2002

STATUS

approved