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A190543 a(n) = 8^n - 3^n.

%I A190543 #44 Apr 01 2025 11:10:31
%S A190543 0,5,55,485,4015,32525,261415,2094965,16770655,134198045,1073682775,
%T A190543 8589757445,68718945295,549754219565,4398041728135,35184357739925,
%U A190543 281474933663935,2251799684545085,18014398122061495,144115186913594405,1152921501120062575,9223372026394422605
%N A190543 a(n) = 8^n - 3^n.
%C A190543 Length-n words from letters {1, 2, ..., 8} with at least one letter greater than 3. - _Joerg Arndt_, Jun 02 2011
%C A190543 All terms are odd multiples of 5, since the powers of 8 mod 10 are 8, 4, 2, 6, ... and the powers of 3 mod 10 are 3, 9, 7, 1, ... - _Alonso del Arte_, Feb 25 2014
%H A190543 Vincenzo Librandi, <a href="/A190543/b190543.txt">Table of n, a(n) for n = 0..300</a>
%H A190543 Feryal Alayont and Evan Henning, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL26/Alayont/ala4.html">Edge Covers of Caterpillars, Cycles with Pendants, and Spider Graphs</a>, J. Int. Seq. (2023) Vol. 26, Art. 23.9.4.
%H A190543 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-24).
%F A190543 a(n) = 11*a(n-1) - 24*a(n-2).
%F A190543 a(n) = A001018(n) - A000244(n). - _Michel Marcus_, Feb 26 2014
%F A190543 From _Vincenzo Librandi_, Oct 05 2014: (Start)
%F A190543 G.f.: 5*x/((1-3*x)*(1-8*x)).
%F A190543 a(n+1) = 5*A016140(n). (End)
%F A190543 E.g.f.: 2*exp(11*x/2)*sinh(5*x/2). - _Elmo R. Oliveira_, Mar 31 2025
%p A190543 A190543:=n->8^n - 3^n; seq(A190543(n), n=0..20); # _Wesley Ivan Hurt_, Feb 26 2014
%t A190543 Table[8^n - 3^n, {n, 0, 19}] (* _Alonso del Arte_, Feb 25 2014 *)
%t A190543 CoefficientList[Series[5 x/((1 - 3 x) (1 - 8 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 05 2014 *)
%o A190543 (Magma) [8^n - 3^n: n in [0..30]];
%o A190543 (PARI) a(n)=8^n-3^n \\ _Charles R Greathouse IV_, Jun 02 2011
%Y A190543 Cf. A000244, A001018, A016140, A016177.
%K A190543 nonn,easy
%O A190543 0,2
%A A190543 _Vincenzo Librandi_, Jun 02 2011