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A122554
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Let S(1)={1} and, for n>1 let S(n) be the smallest set containing x, 2x and x+2 for each element x in S(n-1). a(n) is the number of elements in S(n).
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5
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1, 3, 6, 10, 15, 23, 35, 54, 84, 132, 209, 333, 533, 856, 1378, 2222, 3587, 5795, 9367, 15146, 24496, 39624, 64101, 103705, 167785, 271468, 439230, 710674, 1149879, 1860527, 3010379, 4870878, 7881228
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| If the set mapping has x -> x,2x,x^2 is used instead of x -> x,x+2,2x, the corresponding sequence consists of the Fibonacci numbers 1,2,3,5,8,...
Apparently a(n)= 3*a(n-1) -2*a(n-2) -a(n-3) +a(n-4) for n>6, equivalent to a(n)=A000032(n)+n-1 for n>2. [From R. J. Mathar (mathar(AT)strw.leidenuniv.n), Nov 18 2009]
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EXAMPLE
| Under the indicated set mapping we have {1} -> {1,2,3} -> {1,2,3,4,5,6} -> {1,2,3,4,5,6,7,8,10,12},..., so a(2)=3, a(3)=6, a(4)=10, etc.
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MATHEMATICA
| Do[ Print@ Length@ Nest[ Union@ Flatten[ # /. a_Integer -> {a, 2a, a + 2}] &, {1}, n], {n, 0, 32}] - Robert G. Wilson v Sep 27 2006
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CROSSREFS
| Sequence in context: A143963 A139714 A063542 * A111734 A117457 A024674
Adjacent sequences: A122551 A122552 A122553 * A122555 A122556 A122557
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KEYWORD
| nonn
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AUTHOR
| John W. Layman (layman(AT)math.vt.edu), Sep 20 2006
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EXTENSIONS
| a(17) - a(33) from Robert G. Wilson v Sep 27 2006
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