A135162 a(n) = 7^n - 5^n - 3^n + 2^n. Constants are the prime numbers in decreasing order.

0, 1, 19, 199, 1711, 13471, 101359, 743359, 5367871, 38381311, 272651599, 1928323519, 13596619231, 95666721151, 672114790639, 4717029615679, 33080299697791, 231867445524991, 1624598513486479, 11379820537307839, 79696895380235551, 558069016466824831, 3907436831415107119

Offset: 0

Author

Omar E. Pol, Nov 21 2007

Keywords

• nonn
• easy

Examples

			a(4) = 1711 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401-625-81+16 = 1711.
		

Links

• Vincenzo Librandi, 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},{0,1,19,199},30] (* Harvey P. Dale, Dec 13 2013 *)
CoefficientList[Series[1/(1 - 7 x) - 1/(1 - 5 x) - 1/(1 - 3 x) + 1/(1 - 2 x), {x, 0, 40}], x] (* Vincenzo Librandi, May 22 2014 *)

PARI

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

Formula

a(n) = 7^n - 5^n - 3^n + 2^n.

a(0)=0, a(1)=1, a(2)=19, a(3)=199, a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4). - Harvey P. Dale, Dec 13 2013

G.f.: 1/(1-7*x) - 1/(1-5*x) - 1/(1-3*x) + 1/(1-2 x). - Vincenzo Librandi, May 22 2014

E.g.f.: exp(7*x) - exp(5*x) - exp(3*x) + exp(2*x). - G. C. Greubel, Sep 30 2016

Extensions

More terms from Vincenzo Librandi, Dec 14 2010