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A110678
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a(n) = -n^2 - n + 72.
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1
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72, 70, 66, 60, 52, 42, 30, 16, 0, -18, -38, -60, -84, -110, -138, -168, -200, -234, -270, -308, -348, -390, -434, -480, -528, -578, -630, -684, -740, -798, -858, -920, -984, -1050, -1118, -1188, -1260, -1334, -1410, -1488, -1568, -1650, -1734, -1820, -1908, -1998, -2090, -2184, -2280, -2378, -2478, -2580, -2684, -2790
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OFFSET
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0,1
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COMMENTS
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An example of the sequence of the difference of pronics. This is analogous to the difference of squares. Start at a pronic (72 in this case) and subtract successive pronics.
This is useful in finding prime numbers. As one varies the initial pronic all the even numbers are generated.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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From Chai Wah Wu, Jun 08 2016: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
G.f.: 2*(36 - 73*x + 36*x^2)/(1 - x)^3. (End)
E.g.f.: (72 - 2*x - x^2)*exp(x). - G. C. Greubel, Sep 05 2017
a(n) = 72 - A002378(n). - Michel Marcus, Sep 06 2017
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EXAMPLE
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a(3) = 72 - pronic(3) = 72 - 6 = 66.
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MATHEMATICA
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Table[72 - n*(n + 1), {n, 0, 50}] (* G. C. Greubel, Sep 05 2017 *)
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PROG
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(PARI) a(n)=-n^2-n+72 \\ Charles R Greathouse IV, Jun 17 2017
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CROSSREFS
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Cf. A002378.
Sequence in context: A035879 A033392 A304262 * A008943 A003898 A133899
Adjacent sequences: A110675 A110676 A110677 * A110679 A110680 A110681
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KEYWORD
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easy,sign
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AUTHOR
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Stuart M. Ellerstein (ellerstein(AT)aol.com), Sep 14 2005
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EXTENSIONS
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Edited by Charles R Greathouse IV, Jul 25 2010
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STATUS
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approved
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