A190541 a(n) = 7^n - 3^n.

0, 4, 40, 316, 2320, 16564, 116920, 821356, 5758240, 40333924, 282416200, 1977149596, 13840755760, 96887416084, 678218289880, 4747547161036, 33232887522880, 232630384847044, 1628413210489960, 11398894023111676, 79792262810827600, 558545853622930804, 3909821017201928440

Offset: 0

Author

Vincenzo Librandi, Jun 02 2011

Keywords

• nonn
• easy

Comments

Length-n words from letters {1,2,...,7} with at least one letter greater than 3. - Joerg Arndt, Jun 02 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (10,-21).

Crossrefs

Cf. A000244, A000420.

Similar sequences: A121213, A016169.

Programs

Magma

[7^n - 3^n: n in [0..30]];

Maple

A190541:=n->7^n-3^n: seq(A190541(n), n=0..25); # Wesley Ivan Hurt, Oct 04 2014

Mathematica

Table[7^n - 3^n, {n, 0, 25}] (* or *) CoefficientList[Series[4 x /((1 - 3 x) (1 - 7 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 04 2014 *)
LinearRecurrence[{10,-21},{0,4},20] (* Harvey P. Dale, Mar 30 2015 *)

PARI

a(n)=7^n-3^n \\ Charles R Greathouse IV, Jun 02 2011

Formula

a(n) = 10*a(n-1) - 21*a(n-2).

G.f.: 4*x/((1-3*x)*(1-7*x)). - Vincenzo Librandi, Oct 04 2014

a(n) = A000420(n) - A000244(n). - Wesley Ivan Hurt, Oct 04 2014

E.g.f.: 2*exp(5*x)*sinh(2*x). - Elmo R. Oliveira, Mar 31 2025

a(n) = 4*A016138(n-1). - R. J. Mathar, Jun 07 2025