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A239129
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a(n) = 18*n - 1, n >= 1, the second column of triangle A239127 related to the Collatz problem.
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5
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17, 35, 53, 71, 89, 107, 125, 143, 161, 179, 197, 215, 233, 251, 269, 287, 305, 323, 341, 359, 377, 395, 413, 431, 449, 467, 485, 503, 521, 539, 557, 575, 593, 611, 629, 647, 665, 683, 701, 719, 737, 755, 773, 791, 809, 827, 845, 863, 881
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OFFSET
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1,1
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COMMENTS
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This sequence gives all ending values a(n) (in increasing order) of Collatz sequences of length 5 following the pattern (ud)^2, with u (for `up'), mapping an odd number m to 3*m+1, and d (for `down'), mapping an even number m to m/2. The last entry of this sequence is required to be odd. The first entry is also odd and is given by M(2,n) = 8*n-1 from the array A239126.
This appears as N in Example 2.2. for x=y = 2 in the M. Trümper paper on p. 7, given as a link below.
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LINKS
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FORMULA
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a(n) = 18*n - 1 for n >= 1.
O.g.f.: x*(x+17)/(1-x)^2.
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EXAMPLE
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a(1) = 17 because the Collatz sequence for M(2,1) = 8*1 - 1 = 7 from A239126 is [7, 22, 11, 34, 17] ending in the odd number 17.
a(4) = 71 with the Collatz sequence of length 5 starting with M(2,4) = 31 given by [31, 94, 47, 142, 71], ending in a(4).
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MATHEMATICA
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CoefficientList[Series[(x + 17)/(1 - x)^2, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 16 2014 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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