A009976 Powers of 32.

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

Offset

0,2

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

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).

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

Example

a(6) = 32^6 = 1073741824.

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 *)

Prog

(Sage) [lucas_number1(n, 32, 0) for n in range(1, 17)]# - Zerinvary Lajos, Nov 07 2009
(Magma)[32^n: n in [0..100]] - Vincenzo Librandi, Nov 21 2010
(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

Crossrefs

Subsequence of A000079.

Sequence in context: A223566 A227593 A171306 * A144319 A041481 A158685

Adjacent sequences: A009973 A009974 A009975 * A009977 A009978 A009979

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved