login
A009992
Powers of 48: a(n) = 48^n.
11
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
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
KEYWORD
nonn,easy
EXTENSIONS
Edited by M. F. Hasler, Apr 19 2015
STATUS
approved