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%I #20 Sep 06 2017 03:31:31
%S 72,70,66,60,52,42,30,16,0,-18,-38,-60,-84,-110,-138,-168,-200,-234,
%T -270,-308,-348,-390,-434,-480,-528,-578,-630,-684,-740,-798,-858,
%U -920,-984,-1050,-1118,-1188,-1260,-1334,-1410,-1488,-1568,-1650,-1734,-1820,-1908,-1998,-2090,-2184,-2280,-2378,-2478,-2580,-2684,-2790
%N a(n) = -n^2 - n + 72.
%C 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.
%C This is useful in finding prime numbers. As one varies the initial pronic all the even numbers are generated.
%H G. C. Greubel, <a href="/A110678/b110678.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _Chai Wah Wu_, Jun 08 2016: (Start)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.
%F G.f.: 2*(36 - 73*x + 36*x^2)/(1 - x)^3. (End)
%F E.g.f.: (72 - 2*x - x^2)*exp(x). - _G. C. Greubel_, Sep 05 2017
%F a(n) = 72 - A002378(n). - _Michel Marcus_, Sep 06 2017
%e a(3) = 72 - pronic(3) = 72 - 6 = 66.
%t Table[72 - n*(n + 1), {n,0,50}] (* _G. C. Greubel_, Sep 05 2017 *)
%o (PARI) a(n)=-n^2-n+72 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. A002378.
%K easy,sign
%O 0,1
%A Stuart M. Ellerstein (ellerstein(AT)aol.com), Sep 14 2005
%E Edited by _Charles R Greathouse IV_, Jul 25 2010
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