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

0,3

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).

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

Example

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

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 *)

Prog

(Magma) [7^n-5^n-3^n+2^n: n in [0..50]]; // Vincenzo Librandi, Dec 14 2010
(PARI) a(n) = 7^n - 5^n - 3^n + 2^n \\ Charles R Greathouse IV, Sep 30 2016

Crossrefs

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

Sequence in context: A164890 A066007 A147830 * A185687 A067272 A065582

Adjacent sequences: A135159 A135160 A135161 * A135163 A135164 A135165

Keyword

nonn,easy

Author

Omar E. Pol, Nov 21 2007

Extensions

More terms from Vincenzo Librandi, Dec 14 2010

Status

approved