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

0,2

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).

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

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 *)

Prog

(Magma)[48^n: n in [0..20]] // Vincenzo Librandi, Nov 21 2010
(PARI) A009992(n)=48^n \\ M. F. Hasler, Apr 19 2015
(GAP) List([0..20], n->48^n); # Muniru A Asiru, Nov 21 2018
(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

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).

Sequence in context: A263504 A158783 A227139 * A042105 A206046 A079240

Adjacent sequences: A009989 A009990 A009991 * A009993 A009994 A009995

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Edited by M. F. Hasler, Apr 19 2015

Status

approved