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
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