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A005057 a(n) = 5^n - 2^n.

%I A005057 #51 Nov 17 2023 11:56:29
%S A005057 0,3,21,117,609,3093,15561,77997,390369,1952613,9764601,48826077,
%T A005057 244136529,1220694933,6103499241,30517545357,152587825089,
%U A005057 762939322053,3814697003481,19073485803837,95367430592049,476837156105973,2384185786821321,11920928946689517
%N A005057 a(n) = 5^n - 2^n.
%C A005057 Binomial transform of A024036. - _Wesley Ivan Hurt_, Apr 04 2014
%D A005057 P. P. Patwardhan, Discrete Structures, Technical Publications Pune, 2009 (first ed.), Section 4.27.1.2, p. 110 (Example 4.44-i).
%H A005057 Ivan Panchenko, <a href="/A005057/b005057.txt">Table of n, a(n) for n = 0..200</a>
%H A005057 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 A005057 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-10).
%F A005057 a(n) = A000351(n) - A000079(n). - _R. J. Mathar_, May 07 2008
%F A005057 G.f.: 1/(1-5*x)-1/(1-2*x);
%F A005057 E.g.f.: e^(5*x)-e^(2*x). - _Mohammad K. Azarian_, Jan 14 2009
%F A005057 a(n) = 7*a(n-1)-10*a(n-2), a(0)=0, a(1)=3. - _Vincenzo Librandi_, Dec 30 2010
%F A005057 a(n+1) = 3 * A016127(n). - _Vladimir Joseph Stephan Orlovsky_, Jun 28 2011
%p A005057 A005057:=n->5^n - 2^n; seq(A005057(n), n=0..50); # _Wesley Ivan Hurt_, Apr 04 2014
%t A005057 Table[5^n - 2^n, {n, 0, 60}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 27 2011 *)
%o A005057 (Sage) [5^n - 2^n for n in range(0,21)] # _Zerinvary Lajos_, Jun 04 2009
%o A005057 (Magma) [ 5^n-2^n: n in [0..24] ];
%o A005057 (PARI) a(n)=5^n-1<<n \\ _Charles R Greathouse IV_, Jun 28 2011
%K A005057 nonn,easy
%O A005057 0,2
%A A005057 _N. J. A. Sloane_, Jun 14 1998