%I #64 Jul 12 2023 12:50:04

%S 1,48,2304,110592,5308416,254803968,12230590464,587068342272,

%T 28179280429056,1352605460594688,64925062108545024,

%U 3116402981210161152,149587343098087735296,7180192468708211294208,344649238497994142121984,16543163447903718821855232

%N Powers of 48: a(n) = 48^n.

%C 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.

%C 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

%C 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

%H T. D. Noe, <a href="/A009992/b009992.txt">Table of n, a(n) for n = 0..100</a>

%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (48).

%F G.f.: 1/(1-48*x). - _Philippe Deléham_, Nov 24 2008

%F a(n) = 48^n; a(n) = 48*a(n-1), a(0)=1. - _Vincenzo Librandi_, Nov 21 2010

%F E.g.f.: exp(48*x). - _Muniru A Asiru_, Nov 21 2018

%p A009992 := n -> 48^n: seq(A009992(n), n=0..20); # _M. F. Hasler_, Apr 19 2015

%t 48^Range[0, 15] (* _Michael De Vlieger_, Jan 13 2018 *)

%o (Magma)[48^n: n in [0..20]] // _Vincenzo Librandi_, Nov 21 2010

%o (PARI) A009992(n)=48^n \\ _M. F. Hasler_, Apr 19 2015

%o (GAP) List([0..20],n->48^n); # _Muniru A Asiru_, Nov 21 2018

%o (Python) for n in range(0,20): print(48**n, end=', ') # _Stefano Spezia_, Nov 21 2018

%o (Sage) [(48)^n for n in range(20)] # _G. C. Greubel_, Nov 21 2018

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

%Y 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).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E Edited by _M. F. Hasler_, Apr 19 2015