login
A056452
a(n) = 6^floor((n+1)/2).
9
1, 6, 6, 36, 36, 216, 216, 1296, 1296, 7776, 7776, 46656, 46656, 279936, 279936, 1679616, 1679616, 10077696, 10077696, 60466176, 60466176, 362797056, 362797056, 2176782336, 2176782336, 13060694016, 13060694016, 78364164096
OFFSET
0,2
COMMENTS
Number of achiral rows of length n using up to six different colors. For a(3) = 36, the rows are AAA, ABA, ACA, ADA, AEA, AFA, BAB, BBB, BCB, BDB, BEB, BFB, CAC, CBC, CCC, CDC, CEC, CFC, DAD, DBD, DCD, DDD, DED, DFD, EAE, EBE, ECE, EDE, EEE, EFE, FAF, FBF, FCF, FDF, FEF, and FFF. - Robert A. Russell, Nov 08 2018
Also: a(n) is the number of palindromes with n digits using a maximum of six different symbols. - David A. Corneth, 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]
FORMULA
a(n) = 6^floor((n+1)/2).
a(n) = 6*a(n-2). - Colin Barker, May 06 2012
G.f.: (1+6*x) / (1-6*x^2). - Colin Barker, May 06 2012 [Adapted to offset 0 by Robert A. Russell, Nov 08 2018]
a(n) = C(6,0)*A000007(n) + C(6,1)*A057427(n) + C(6,2)*A056453(n) + C(6,3)*A056454(n) + C(6,4)*A056455(n) + C(6,5)*A056456(n) + C(6,6)*A056457(n). - Robert A. Russell, Nov 08 2018
MAPLE
A056452:=n->6^floor((n+1)/2);
MATHEMATICA
Riffle[6^Range[0, 20], 6^Range[20]] (* Harvey P. Dale, Jun 18 2017 *)
Table[6^Ceiling[n/2], {n, 0, 40}] (* or *)
LinearRecurrence[{0, 6}, {1, 6}, 40] (* Robert A. Russell, Nov 08 2018 *)
PROG
(Magma) [6^Floor((n+1)/2): n in [0..40]]; // Vincenzo Librandi, Aug 16 2011
CROSSREFS
Column k=6 of A321391.
Cf. A016116.
Cf. A000400 (oriented), A056308 (unoriented), A320524 (chiral).
Sequence in context: A111437 A056464 A056454 * A183622 A176861 A377204
KEYWORD
nonn,easy
EXTENSIONS
a(0)=1 prepended by Robert A. Russell, Nov 08 2018
Name corrected by David A. Corneth, Nov 08 2018
STATUS
approved