A009972 Powers of 28.

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

Offset

0,2

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).

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)

Mathematica

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

Prog

(SageMath) [lucas_number1(n, 28, 0) for n in range(1, 17)] # Zerinvary Lajos, Apr 29 2009
(Magma) [28^n: n in [0..100]]; // Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=28^n \\ Charles R Greathouse IV, Sep 28 2015

Crossrefs

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

Sequence in context: A189775 A189157 A267732 * A114037 A041365 A042514

Adjacent sequences: A009969 A009970 A009971 * A009973 A009974 A009975

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved