A009992 Powers of 48: a(n) = 48^n.

1, 48, 2304, 110592, 5308416, 254803968, 12230590464, 587068342272, 28179280429056, 1352605460594688, 64925062108545024, 3116402981210161152, 149587343098087735296, 7180192468708211294208, 344649238497994142121984, 16543163447903718821855232

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Same as Pisot sequences E(1, 48), L(1, 48), P(1, 48), T(1, 48). Essentially same as Pisot sequences E(48, 2304), L(48, 2304), P(48, 2304), T(48, 2304). See A008776 for definitions of Pisot sequences.

If X_1, X_2, ..., X_n is a partition of the set {1,2,...,2*n} into blocks of size 2 then, for n>=1, a(n) is equal to the number of functions f : {1,2,..., 2*n}->{1,2,3,4,5,6,7} such that for fixed y_1,y_2,...,y_n in {1,2,3,4,5,6,7} we have f(X_i)<>{y_i}, (i=1,2,...,n). - Milan Janjic, May 24 2007

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 48-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
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (48).

Crossrefs

Cf. A001018 (powers of 8), ..., A001029 (powers of 19), A009964 (powers of 20), ..., A009991 (powers of 47), A087752 (powers of 49).

Cf. A000079 (2^n), A000244 (3^n), A000302 (4^n), A000400 (6^n), A001018 (8^n), A001021 (12^n), A001025 (16^n), A009968 (24^n).

Programs

GAP

List([0..20],n->48^n); # Muniru A Asiru, Nov 21 2018

Magma

[48^n: n in [0..20]] // Vincenzo Librandi, Nov 21 2010

Maple

A009992 := n -> 48^n: seq(A009992(n), n=0..20); # M. F. Hasler, Apr 19 2015

Mathematica

48^Range[0, 15] (* Michael De Vlieger, Jan 13 2018 *)

PARI

A009992(n)=48^n \\ M. F. Hasler, Apr 19 2015

Python

for n in range(0,20): print(48**n, end=', ') # Stefano Spezia, Nov 21 2018

Sage

[(48)^n for n in range(20)] # G. C. Greubel, Nov 21 2018

Formula

G.f.: 1/(1-48*x). - Philippe Deléham, Nov 24 2008

a(n) = 48^n; a(n) = 48*a(n-1), a(0)=1. - Vincenzo Librandi, Nov 21 2010

E.g.f.: exp(48*x). - Muniru A Asiru, Nov 21 2018

Extensions

Edited by M. F. Hasler, Apr 19 2015