A056452 a(n) = 6^floor((n+1)/2).

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]

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..2000

Index entries for linear recurrences with constant coefficients, signature (0,6).

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 A245131

Adjacent sequences: A056449 A056450 A056451 * A056453 A056454 A056455

Keyword

nonn,easy

Author

Marks R. Nester

Extensions

a(0)=1 prepended by Robert A. Russell, Nov 08 2018

Name corrected by David A. Corneth, Nov 08 2018

Status

approved