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

0, 3, 21, 117, 609, 3093, 15561, 77997, 390369, 1952613, 9764601, 48826077, 244136529, 1220694933, 6103499241, 30517545357, 152587825089, 762939322053, 3814697003481, 19073485803837, 95367430592049, 476837156105973, 2384185786821321, 11920928946689517

Offset: 0

Author

N. J. A. Sloane, Jun 14 1998

Keywords

• nonn
• easy

Comments

Binomial transform of A024036. - Wesley Ivan Hurt, Apr 04 2014

References

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

Links

• Ivan Panchenko, Table of n, a(n) for n = 0..200
• Feryal Alayont and Evan Henning, Edge Covers of Caterpillars, Cycles with Pendants, and Spider Graphs, J. Int. Seq. (2023) Vol. 26, Art. 23.9.4.
• Index entries for linear recurrences with constant coefficients, signature (7,-10).

Programs

Magma

[ 5^n-2^n: n in [0..24] ];

Maple

A005057:=n->5^n - 2^n; seq(A005057(n), n=0..50); # Wesley Ivan Hurt, Apr 04 2014

Mathematica

Table[5^n - 2^n, {n, 0, 60}] (* Vladimir Joseph Stephan Orlovsky, Jun 27 2011 *)

PARI

a(n)=5^n-1<Charles R Greathouse IV, Jun 28 2011

Sage

[5^n - 2^n for n in range(0,21)] # Zerinvary Lajos, Jun 04 2009

Formula

a(n) = A000351(n) - A000079(n). - R. J. Mathar, May 07 2008

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

E.g.f.: e^(5*x)-e^(2*x). - Mohammad K. Azarian, Jan 14 2009

a(n) = 7*a(n-1)-10*a(n-2), a(0)=0, a(1)=3. - Vincenzo Librandi, Dec 30 2010

a(n+1) = 3 * A016127(n). - Vladimir Joseph Stephan Orlovsky, Jun 28 2011