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%I #32 Sep 08 2022 08:45:32
%S 0,3,29,237,1841,13893,102689,747477,5380481,38419653,272767649,
%T 1928673717,13597673921,95669893413,672124323809,4717058247957,
%U 33080385660161,231867703543173,1624599287803169,11379822860782197,79696902351707201,558069037383336933,3907436894168837729
%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="/A135163/b135163.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) = 1841 because 7^4 = 2401, 5^4 = 625, 3^4 = 81, 2^4 = 16 and 2401-625+81-16 = 1841.
%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 LinearRecurrence[{17,-101,247,-210},{0,3,29,237},30] (* _Harvey P. Dale_, Sep 17 2016 *)
%o (Magma) [7^n-5^n+3^n-2^n: n in [0..50]]; // _Vincenzo Librandi_, Dec 14 2010
%o (Magma) I:=[0, 3, 29, 237]; [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 0,2
%A _Omar E. Pol_, Nov 21 2007
%E More terms from _Vincenzo Librandi_, Dec 14 2010
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