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
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by M. F. Hasler, Apr 19 2015
STATUS
approved