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Search: id:A123212
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| A123212 |
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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 sum of the elements in S(n). |
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1
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| 1, 3, 7, 31, 383, 71679, 4313284607, 18447026747376402431, 340282367000167840050178713574329810943
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OFFSET
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1,2
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COMMENT
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If we take the cardinality of the set S(n) instead of the sum, we get the Fibonacci numbers 1,2,3,5,8,13,21,34,... If the set mapping uses x -> x, 2x, and 3x instead of x -> x, 2x, anx x^2, the corrresponding sequence consists of the Stirling numbers of the second kind 1,6,25,90,301,966,3025,... (A000392).
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EXAMPLE
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Under the indicated set mapping we have {1} -> {1,2} -> {1,2,4} -> {1,2,4,8,16}, giving the sums a(1)=1, a(2)=3, a(3)=7, a(4)=31, etc.
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CROSSREFS
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Cf. A000045, A000392, A122554.
Adjacent sequences: A123209 A123210 A123211 this_sequence A123213 A123214 A123215
Sequence in context: A074047 A121810 A081475 this_sequence A070231 A096239 A074699
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KEYWORD
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nonn
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AUTHOR
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John W. Layman (layman(AT)math.vt.edu), Oct 05 2006
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