A110678 a(n) = -n^2 - n + 72.

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

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