OFFSET
0,2
COMMENTS
One followed by powers of 3 with positive exponent, repeated. - Omar E. Pol, Jul 27 2009
Number of achiral rows of n colors using up to three colors. E.g., for a(3) = 9, the rows are AAA, ABA, ACA, BAB, BBB, BCB, CAC, CBC, and CCC. - Robert A. Russell, Nov 07 2018
REFERENCES
M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Index entries for linear recurrences with constant coefficients, signature (0,3).
FORMULA
G.f.: (1 + 3*x) / (1 - 3*x^2). - R. J. Mathar, Jul 06 2011 [Adapted to offset 0 by Robert A. Russell, Nov 07 2018]
a(n) = k^ceiling(n/2), where k = 3 is the number of possible colors. - Robert A. Russell, Nov 07 2018
a(n) = C(3,0)*A000007(n) + C(3,1)*A057427(n) + C(3,2)*A056453(n) + C(3,3)*A056454(n). - Robert A. Russell, Nov 08 2018
E.g.f.: cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x). - Stefano Spezia, Dec 31 2022
MATHEMATICA
Riffle[3^Range[0, 20], 3^Range[20]] (* Harvey P. Dale, Jan 21 2015 *)
Table[3^Ceiling[n/2], {n, 0, 40}] (* or *)
LinearRecurrence[{0, 3}, {1, 3}, 40] (* Robert A. Russell, Nov 07 2018 *)
PROG
(Magma) [3^Floor((n+1)/2): n in [0..40]]; // Vincenzo Librandi, Aug 16 2011
(PARI) a(n)=3^floor((n+1)/2); \\ Joerg Arndt, Apr 23 2013
(Python)
def A056449(n): return 3**(n+1>>1) # Chai Wah Wu, Oct 28 2024
CROSSREFS
Column k=3 of A321391.
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane at the suggestion of Klaus Brockhaus, Jul 03 2009
a(0)=1 prepended by Robert A. Russell, Nov 07 2018
STATUS
approved