A009972 Powers of 28.

1, 28, 784, 21952, 614656, 17210368, 481890304, 13492928512, 377801998336, 10578455953408, 296196766695424, 8293509467471872, 232218265089212416, 6502111422497947648, 182059119829942534144, 5097655355238390956032, 142734349946674946768896, 3996561798506898509529088

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Same as Pisot sequences E(1, 28), L(1, 28), P(1, 28), T(1, 28). Essentially same as Pisot sequences E(28, 784), L(28, 784), P(28, 784), T(28, 784). See A008776 for definitions of Pisot sequences.

The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n >= 1, a(n) equals the number of 28-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Links

• T. D. Noe, Table of n, a(n) for n = 0..100
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (28).

Crossrefs

Cf. A000079, A000302, A000420, A001023, A008776.

Programs

Magma

[28^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010

Mathematica

28^Range[0, 13] (* Alonso del Arte, Feb 28 2015 *)
NestList[28#&,1,20] (* Harvey P. Dale, Jan 19 2019 *)

PARI

a(n)=28^n \\ Charles R Greathouse IV, Sep 28 2015

Sage

[lucas_number1(n,28,0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009

Formula

G.f.: 1/(1-28*x). - Philippe Deléham, Nov 24 2008

a(n) = 28^n; a(n) = 28*a(n-1), n > 0, a(0) = 1. - Vincenzo Librandi, Nov 21 2010

From Elmo R. Oliveira, Jul 10 2025: (Start)

E.g.f.: exp(28*x).

a(n) = A000079(n)*A001023(n) = A000302(n)*A000420(n). (End)