A135164 - OEIS

%I #28 Sep 08 2022 08:45:32

%S 2,7,37,253,1873,13957,102817,747733,5380993,38420677,272769697,

%T 1928677813,13597682113,95669909797,672124356577,4717058313493,

%U 33080385791233,231867703805317,1624599288327457,11379822861830773,79696902353804353,558069037387531237,3907436894177226337

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

%C Constants are the prime numbers in decreasing order.

%H Vincenzo Librandi, <a href="/A135164/b135164.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (17,-101,247,-210).

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

%F From _Vincenzo Librandi_, May 22 2014: (Start)

%F G.f.: 1/(1-7*x) - 1/(1-5*x) + 1/(1-3*x) + 1/(1-2*x).

%F a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4) for n>3. (End)

%F E.g.f.: exp(7*x) - exp(5*x) + exp(3*x) + exp(2*x). - _G. C. Greubel_, Sep 30 2016

%e a(4) = 1873 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401-625+81+16 = 1873.

%t 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 *)

%t Table[7^n-5^n+3^n+2^n,{n,0,30}] (* or *) LinearRecurrence[{17,-101,247,-210},{2,7,37,253},30] (* _Harvey P. Dale_, Jul 23 2016 *)

%o (Magma) [7^n-5^n+3^n+2^n: n in [0..50]]; // _Vincenzo Librandi_, Dec 14 2010

%o (Magma) I:=[2,7,37,253]; [n le 4 select I[n] else 17*Self(n-1)-101*Self(n-2)+247*Self(n-3)-210*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, May 22 2014

%o (PARI) a(n)=7^n-5^n+3^n+2^n \\ _Charles R Greathouse IV_, Sep 30 2016

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

%K nonn,easy

%O 0,1

%A _Omar E. Pol_, Nov 21 2007

%E More terms from _Vincenzo Librandi_, Dec 14 2010