A135159 a(n) = 5^n - 3^n + 2^n.

1, 4, 20, 106, 560, 2914, 14960, 76066, 384320, 1933954, 9707600, 48653026, 243613280, 1219116994, 6098749040, 30503261986, 152544909440, 762810444034, 3814310107280, 19072324590946, 95363945904800, 476826699947074, 2384154414150320, 11920834820287906, 59604362362631360, 298022376621898114

Offset: 0

Author

Omar E. Pol, Nov 21 2007

Keywords

• nonn
• easy

Comments

Constants are the prime numbers in decreasing order.

Examples

			a(4)=560 because 5^4=625, 3^4=81, 2^4=16 and 625-81+16=560.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-31,30).

Crossrefs

Cf. A000079, A000244, A000351, A007689.

Programs

Magma

[5^n-3^n+2^n: n in [0..50]]; // Vincenzo Librandi, Dec 15 2010

Mathematica

lst={};Do[p=5^n-3^n+2^n;AppendTo[lst, p], {n, 0, 7^2}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 19 2008 *)
CoefficientList[Series[1/(1 - 5 x) - 1/(1 - 3 x) + 1/(1 - 2 x), {x, 0, 40}], x] (* Vincenzo Librandi, May 22 2014 *)
Table[5^n - 3^n + 2^n, {n,0,25}] (* or *) LinearRecurrence[{10, -31, 30}, {1, 4, 20}, 25] (* G. C. Greubel, Sep 30 2016 *)

Formula

a(n) = 5^n - 3^n + 2^n.

From Mohammad K. Azarian, Jan 16 2009: (Start)

G.f.: 1/(1-5*x) - 1/(1-3*x) + 1/(1-2*x).

E.g.f.: exp(5*x) - exp(3*x) + exp(2*x). (End)

a(n) = 10*a(n-1) - 31*a(n-2) + 30*a(n-3). - G. C. Greubel, Sep 30 2016

Extensions

More terms from Vincenzo Librandi, Dec 15 2010