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A005057 a(n) = 5^n - 2^n. 15

%I #51 Nov 17 2023 11:56:29

%S 0,3,21,117,609,3093,15561,77997,390369,1952613,9764601,48826077,

%T 244136529,1220694933,6103499241,30517545357,152587825089,

%U 762939322053,3814697003481,19073485803837,95367430592049,476837156105973,2384185786821321,11920928946689517

%N a(n) = 5^n - 2^n.

%C Binomial transform of A024036. - _Wesley Ivan Hurt_, Apr 04 2014

%D P. P. Patwardhan, Discrete Structures, Technical Publications Pune, 2009 (first ed.), Section 4.27.1.2, p. 110 (Example 4.44-i).

%H Ivan Panchenko, <a href="/A005057/b005057.txt">Table of n, a(n) for n = 0..200</a>

%H 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-10).

%F a(n) = A000351(n) - A000079(n). - _R. J. Mathar_, May 07 2008

%F G.f.: 1/(1-5*x)-1/(1-2*x);

%F E.g.f.: e^(5*x)-e^(2*x). - _Mohammad K. Azarian_, Jan 14 2009

%F a(n) = 7*a(n-1)-10*a(n-2), a(0)=0, a(1)=3. - _Vincenzo Librandi_, Dec 30 2010

%F a(n+1) = 3 * A016127(n). - _Vladimir Joseph Stephan Orlovsky_, Jun 28 2011

%p A005057:=n->5^n - 2^n; seq(A005057(n), n=0..50); # _Wesley Ivan Hurt_, Apr 04 2014

%t Table[5^n - 2^n, {n, 0, 60}] (* _Vladimir Joseph Stephan Orlovsky_, Jun 27 2011 *)

%o (Sage) [5^n - 2^n for n in range(0,21)] # _Zerinvary Lajos_, Jun 04 2009

%o (Magma) [ 5^n-2^n: n in [0..24] ];

%o (PARI) a(n)=5^n-1<<n \\ _Charles R Greathouse IV_, Jun 28 2011

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_, Jun 14 1998

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)