A135161 a(n) = 7^n - 5^n - 3^n - 2^n. Constants are the prime numbers in decreasing order.

-2, -3, 11, 183, 1679, 13407, 101231, 743103, 5367359, 38380287, 272649551, 1928319423, 13596611039, 95666704767, 672114757871, 4717029550143, 33080299566719, 231867445262847, 1624598512962191, 11379820536259263, 79696895378138399, 558069016462630527, 3907436831406718511

Offset: 0

Author

Omar E. Pol, Nov 21 2007

Keywords

• easy
• sign

Examples

			a(4) = 1679 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and we can write 2401 -625 -81 -16 = 1679.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (17,-101,247,-210).

Crossrefs

Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.

Programs

Magma

[7^n-5^n-3^n-2^n: n in [0..50]] // Vincenzo Librandi, Dec 14 2010

Mathematica

Table[7^n-5^n-3^n-2^n,{n,0,30}] (* or *) LinearRecurrence[{17,-101,247,-210},{-2,-3,11,183},30] (* Harvey P. Dale, Sep 23 2016 *)

PARI

a(n) = 7^n - 5^n - 3^n - 2^n \\ Charles R Greathouse IV, Sep 30 2016

Formula

From G. C. Greubel, Sep 30 2016: (Start)

a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4).

G.f.: -x*(-2 + 31 x - 140 x^2 + 187 x^3)/((1 -2*x)*(1 -3*x)*(1 -5*x)*(1 -7*x)).

E.g.f.: exp(7*x) - exp(5*x) - exp(3*x) - exp(2*x). (End)

Extensions

More terms from Vincenzo Librandi, Dec 14 2010