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A135165 a(n) = 7^n + 5^n - 3^n - 2^n.

%I A135165 #25 Sep 08 2022 08:45:32
%S A135165 0,7,61,433,2929,19657,132481,899353,6148609,42286537,292180801,
%T A135165 2025975673,14084892289,98108111017,684321789121,4778064706393,
%U A135165 33385475347969,233393324169097,1632227907493441,11417967508915513,79887630241419649,559022690779036777,3912205202988749761
%N A135165 a(n) = 7^n + 5^n - 3^n - 2^n.
%C A135165 Constants are the prime numbers in decreasing order.
%H A135165 Vincenzo Librandi, <a href="/A135165/b135165.txt">Table of n, a(n) for n = 0..1000</a>
%H A135165 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (17,-101,247,-210).
%F A135165 a(n) = 7^n + 5^n - 3^n - 2^n.
%F A135165 From _Vincenzo Librandi_, May 22 2014: (Start)
%F A135165 G.f.: 1/(1-7*x) + 1/(1-5*x) - 1/(1-3*x) - 1/(1-2*x).
%F A135165 a(n) = 17*a(n-1) - 101*a(n-2) + 247*a(n-3) - 210*a(n-4) for n>3. (End)
%F A135165 E.g.f.: exp(7*x) + exp(5*x) - exp(3*x) - exp(2*x). - _G. C. Greubel_, Sep 30 2016
%e A135165 a(4) = 2929 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401+625-81-16 = 2929.
%t A135165 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 A135165 LinearRecurrence[{17,-101,247,-210},{0,7,61,433},30] (* _Harvey P. Dale_, Mar 20 2015 *)
%o A135165 (Magma)[7^n+5^n-3^n-2^n: n in [0..50]]; // _Vincenzo Librandi_, Dec 14 2010
%o A135165 (Magma) I:=[0,7,61,433]; [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 A135165 (PARI) a(n)=7^n+5^n-3^n-2^n \\ _Charles R Greathouse IV_, Sep 30 2016
%Y A135165 Cf. A000079, A000244, A000351, A000420, A001047, A074527, A007689, A135158, A135159, A135160.
%K A135165 nonn,easy
%O A135165 0,2
%A A135165 _Omar E. Pol_, Nov 21 2007