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

0,2

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).

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

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 *)

Prog

(Sage) [5^n - 2^n for n in range(0, 21)] # Zerinvary Lajos, Jun 04 2009
(Magma) [ 5^n-2^n: n in [0..24] ];
(PARI) a(n)=5^n-1<<n \\ Charles R Greathouse IV, Jun 28 2011

Crossrefs

Sequence in context: A183404 A309670 A121140 * A092634 A178537 A084159

Adjacent sequences: A005054 A005055 A005056 * A005058 A005059 A005060

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 14 1998

Status

approved