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A190542 a(n) = 7^n - 4^n.

%I A190542 #27 Nov 13 2024 17:15:17
%S A190542 0,3,33,279,2145,15783,113553,807159,5699265,40091463,281426673,
%T A190542 1973132439,13824509985,96821901543,677954637393,4746487768119,
%U A190542 33228635602305,232613334118023,1628344878433713,11398620307466199,79791166785984225,558541466036772903,3909803456396943633,27368676971336738679,191580949905589703745
%N A190542 a(n) = 7^n - 4^n.
%C A190542 Length-n words from letters {1,2,...,7} with at least one letter greater than 4. - _Joerg Arndt_, Jun 02 2011
%H A190542 Vincenzo Librandi, <a href="/A190542/b190542.txt">Table of n, a(n) for n = 0..300</a>
%H A190542 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-28).
%F A190542 a(n) = 11*a(n-1) - 28*a(n-2).
%F A190542 a(n) = A000420(n) - A000302(n). - _Michel Marcus_, Feb 26 2014
%F A190542 From _G. C. Greubel_, Nov 13 2024: (Start)
%F A190542 G.f.: 3*x/((1-4*x)*(1-7*x)).
%F A190542 E.g.f.: 2*exp(11*x/2)*sinh(3*x/2). (End)
%p A190542 A190542:=n->7^n - 4^n; seq(A190542(n), n=0..30); # _Wesley Ivan Hurt_, Feb 26 2014
%t A190542 Table[7^n - 4^n, {n, 0, 30}] (* _Wesley Ivan Hurt_, Feb 26 2014 *)
%t A190542 LinearRecurrence[{11,-28},{0,3},30] (* _Harvey P. Dale_, Dec 21 2019 *)
%o A190542 (Magma) [7^n -4^n: n in [0..30]];
%o A190542 (PARI) a(n)=7^n-4^n \\ _Charles R Greathouse IV_, Jun 02 2011
%o A190542 (Python)
%o A190542 def A190542(n): return pow(7,n) - pow(4,n)
%o A190542 print([A190542(n) for n in range(31)]) # _G. C. Greubel_, Nov 13 2024
%Y A190542 Cf. A000302, A000420, A016169, A121213.
%K A190542 nonn,easy
%O A190542 0,2
%A A190542 _Vincenzo Librandi_, Jun 02 2011