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A072930
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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).
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1
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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
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1,2
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LINKS
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FORMULA
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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...).
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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