OFFSET
0,2
COMMENTS
Number of achiral rows of n colors using up to five colors. For a(3) = 25, the rows are AAA, ABA, ACA, ADA, AEA, BAB, BBB, BCB, BDB, BEB, CAC, CBC, CCC, CDC, CEC, DAD, DBD, DCD, DDD, DED, EAE, EBE, ECE, EDE, and EEE. - Robert A. Russell, Nov 09 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 (0,5).
FORMULA
a(n) = 5^floor((n+1)/2).
a(n) = 5*a(n-2). - Colin Barker, May 06 2012
G.f.: (1+5*x) / (1-5*x^2). - Colin Barker, May 06 2012 [Adapted to offset 0 by Robert A. Russell, Nov 07 2018]
a(n) = C(5,0)*A000007(n) + C(5,1)*A057427(n) + C(5,2)*A056453(n) + C(5,3)*A056454(n) + C(5,4)*A056455(n) + C(5,5)*A056456(n). - Robert A. Russell, Nov 08 2018
E.g.f.: cosh(sqrt(5)*x) + sqrt(5)*sinh(sqrt(5)*x). - Stefano Spezia, Jun 06 2023
MATHEMATICA
LinearRecurrence[{0, 5}, {1, 5}, 30] (* or *) Riffle[5^Range[0, 20], 5^Range[20]] (* Harvey P. Dale, Jul 28 2018 *)
Table[5^Ceiling[n/2], {n, 0, 40}] (* Robert A. Russell, Nov 07 2018 *)
PROG
(Magma) [5^Floor((n+1)/2): n in [0..40]]; // Vincenzo Librandi, Aug 16 2011
(PARI) vector(40, n, n--; 5^floor((n+1)/2)) \\ G. C. Greubel, Nov 07 2018
CROSSREFS
Column k=5 of A321391.
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
a(0)=1 prepended by Robert A. Russell, Nov 07 2018
STATUS
approved