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A137786 a(n) = 4^n - 3^n - 2^n.

%I A137786 #44 Sep 12 2024 20:34:27
%S A137786 -1,-1,3,29,159,749,3303,14069,58719,241949,988503,4015109,16241679,
%T A137786 65506349,263636103,1059360149,4251855039,17050597949,68331794103,
%U A137786 273715121189,1096023794799,4387584060749,17560800790503,70274592610229,281192530396959,1125052584678749
%N A137786 a(n) = 4^n - 3^n - 2^n.
%C A137786 a(n) mod 100 = 49 for n = 4*k + 1, k > 0; a(n) mod 100 = 3 for n = 4*k + 2, k >= 0. [_Alex Ratushnyak_, Jul 03 2012]
%H A137786 Vincenzo Librandi, <a href="/A137786/b137786.txt">Table of n, a(n) for n = 0..1000</a>
%H A137786 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-26,24).
%F A137786 G.f.: -(1-8*x+14*x^2)/((1-2*x)*(1-3*x)*(1-4*x)). - _Bruno Berselli_, Jul 04 2012
%F A137786 a(0)=-1, a(1)=-1, a(2)=3, a(n) = 9*a(n-1) - 26*a(n-2) + 24*a(n-3). - _Harvey P. Dale_, Sep 19 2012
%F A137786 E.g.f.: exp(2*x)*(exp(2*x) - exp(x) - 1). - _Elmo R. Oliveira_, Sep 12 2024
%p A137786 A137786:=n->4^n - 3^n - 2^n; seq(A137786(n), n=0..25); # _Wesley Ivan Hurt_, Feb 10 2014
%t A137786 Table[4^n - 3^n - 2^n, {n, 0, 25}] (* _Bruno Berselli_, Jul 04 2012 *)
%t A137786 LinearRecurrence[{9,-26,24},{-1,-1,3},30] (* _Harvey P. Dale_, Sep 19 2012 *)
%t A137786 CoefficientList[Series[-(1 - 8 x + 14 x^2)/((1 - 2 x) (1 - 3 x) (1 - 4 x)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 12 2014 *)
%o A137786 (Python)
%o A137786 print([4**n - 3**n - 2**n for n in range(99)])
%o A137786 # _Alex Ratushnyak_, Jul 03 2012
%o A137786 (PARI) a(n) = 4^n-3^n-2^n; \\ _Joerg Arndt_, Jul 04 2012
%o A137786 (Magma) I:=[-1,-1,3]; [n le 3 select I[n] else 9*Self(n-1)-26*Self(n-2)+24*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Feb 12 2014
%Y A137786 Cf. A001047, A005061, A074526, A083324, A147975.
%K A137786 sign,easy
%O A137786 0,3
%A A137786 _Vladimir Joseph Stephan Orlovsky_, Apr 28 2008
%E A137786 Offset set to 0, terms corrected, more terms added by _Alex Ratushnyak_, Jul 03 2012.