A009976 Powers of 32.

1, 32, 1024, 32768, 1048576, 33554432, 1073741824, 34359738368, 1099511627776, 35184372088832, 1125899906842624, 36028797018963968, 1152921504606846976, 36893488147419103232, 1180591620717411303424, 37778931862957161709568, 1208925819614629174706176, 38685626227668133590597632

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Same as Pisot sequences E(1, 32), L(1, 32), P(1, 32), T(1, 32). Essentially same as Pisot sequences E(32, 1024), L(32, 1024), P(32, 1024), T(32, 1024). 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 32-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011

Examples

			a(6) = 32^6 = 1073741824.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..100
• Philip DeOrsey, Stephen G. Hartke, and Jason Williford, A Classification of Hyperfocused 12-Arcs, arXiv:2105.08300 [math.CO], 2021.
• Tanya Khovanova, Recursive Sequences.
• Index entries for linear recurrences with constant coefficients, signature (32).

Crossrefs

Subsequence of A000079.

Cf. A001025, A008587, A008776, A089357.

Programs

Magma

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

Maple

A009976:=n->32^n; seq(A009976(k), k=0..50); # Wesley Ivan Hurt, Nov 04 2013

Mathematica

Table[32^n, {n,0,50}] (* Wesley Ivan Hurt, Nov 04 2013 *)

Maxima

A009976(n):=32^n$
makelist(A009976(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI

a(n)=32^n \\ Charles R Greathouse IV, Sep 24 2015

Python

def A009976(n): return 1<<5*n # Chai Wah Wu, Nov 10 2022

SageMath

[lucas_number1(n,32,0) for n in range(1, 17)] # Zerinvary Lajos, Nov 07 2009

Formula

G.f.: 1/(1-32*x). - Philippe Deléham, Nov 24 2008

a(n) = 32^n; a(n) = 32*a(n-1) for n > 0, a(0)=1. - Vincenzo Librandi, Nov 21 2010

From Elmo R. Oliveira, Jul 08 2025: (Start)

E.g.f.: exp(32*x).

a(n) = 2^A008587(n) = A000079(n)*A001025(n) = A089357(n)/A000079(n). (End)