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

%I A135162 #25 Sep 08 2022 08:45:32
%S A135162 0,1,19,199,1711,13471,101359,743359,5367871,38381311,272651599,
%T A135162 1928323519,13596619231,95666721151,672114790639,4717029615679,
%U A135162 33080299697791,231867445524991,1624598513486479,11379820537307839,79696895380235551,558069016466824831,3907436831415107119
%N A135162 a(n) = 7^n - 5^n - 3^n + 2^n. Constants are the prime numbers in decreasing order.
%H A135162 Vincenzo Librandi, <a href="/A135162/b135162.txt">Table of n, a(n) for n = 0..1000</a>
%H A135162 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (17,-101,247,-210).
%F A135162 a(n) = 7^n - 5^n - 3^n + 2^n.
%F A135162 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
%F A135162 G.f.: 1/(1-7*x) - 1/(1-5*x) - 1/(1-3*x) + 1/(1-2 x). - _Vincenzo Librandi_, May 22 2014
%F A135162 E.g.f.: exp(7*x) - exp(5*x) - exp(3*x) + exp(2*x). - _G. C. Greubel_, Sep 30 2016
%e A135162 a(4) = 1711 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401-625-81+16 = 1711.
%t A135162 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 *)
%t A135162 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 *)
%o A135162 (Magma) [7^n-5^n-3^n+2^n: n in [0..50]]; // _Vincenzo Librandi_, Dec 14 2010
%o A135162 (PARI) a(n) = 7^n - 5^n - 3^n + 2^n \\ _Charles R Greathouse IV_, Sep 30 2016
%Y A135162 Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.
%K A135162 nonn,easy
%O A135162 0,3
%A A135162 _Omar E. Pol_, Nov 21 2007
%E A135162 More terms from _Vincenzo Librandi_, Dec 14 2010