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 A110678 a(n) = -n^2 - n + 72. 1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS 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. LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA 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 EXAMPLE a(3) = 72 - pronic(3) = 72 - 6 = 66. MATHEMATICA Table[72 - n*(n + 1), {n, 0, 50}] (* G. C. Greubel, Sep 05 2017 *) PROG (PARI) a(n)=-n^2-n+72 \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A002378. Sequence in context: A035879 A033392 A304262 * A008943 A003898 A133899 Adjacent sequences:  A110675 A110676 A110677 * A110679 A110680 A110681 KEYWORD easy,sign AUTHOR Stuart M. Ellerstein (ellerstein(AT)aol.com), Sep 14 2005 EXTENSIONS Edited by Charles R Greathouse IV, Jul 25 2010 STATUS approved

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Last modified December 7 03:27 EST 2019. Contains 329836 sequences. (Running on oeis4.)