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A009992 Powers of 48. 10
1, 48, 2304, 110592, 5308416, 254803968, 12230590464, 587068342272, 28179280429056, 1352605460594688, 64925062108545024, 3116402981210161152, 149587343098087735296, 7180192468708211294208, 344649238497994142121984, 16543163447903718821855232 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

MAPLE

A009992 := n -> 49^n; # M. F. Hasler, Apr 19 2015

PROG

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

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

CROSSREFS

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

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

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Last modified April 28 05:37 EDT 2017. Contains 285557 sequences.