OFFSET
0,3
COMMENTS
The finite sequence [1,2,3,4,9,8,27] is used in Timaios [35b] by Platon.
REFERENCES
Luc Brisson, Le Même et l'Autre dans la Structure Ontologique du Timée de Platon, Klincksieck, Paris, 1974, p. 317.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,5,0,-6).
FORMULA
a(2*k) = 2^k, a(2*k+1) = 3^k, k>=0.
G.f.: (1+x-3*x^2-2*x^3)/((1-2*x^2)*(1-3*x^2)).
a(n) = ((5-(-1)^n)/2)^((2*n-1+(-1)^n)/4). - Luce ETIENNE, Dec 13 2014
MAPLE
seq(seq(k^n, k=2..3), n=0..19); # Zerinvary Lajos, Jun 29 2007
MATHEMATICA
With[{nn=20}, Riffle[2^Range[0, nn], 3^Range[0, nn]]] (* Harvey P. Dale, Nov 28 2011 *)
Flatten[Table[{2^n, 3^n}, {n, 0, 20}]] (* Vincenzo Librandi, May 10 2015 *)
PROG
(Magma) &cat[ [2^n, 3^n]: n in [0..30]]; // Vincenzo Librandi, May 10 2015
(Python)
def A098293(n): return 3**(n>>1) if n&1 else 1<<(n>>1) # Chai Wah Wu, Sep 24 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Oct 18 2004
STATUS
approved